diff --git a/exporters/metric/internal/statsd/conn.go b/exporters/metric/internal/statsd/conn.go
index ba28386b329..4b8214cf6fc 100644
--- a/exporters/metric/internal/statsd/conn.go
+++ b/exporters/metric/internal/statsd/conn.go
@@ -163,16 +163,15 @@ func (e *Exporter) Export(_ context.Context, checkpointSet export.CheckpointSet)
 	var aggErr error
 	var sendErr error
 
-	checkpointSet.ForEach(func(rec export.Record) {
+	aggErr = checkpointSet.ForEach(func(rec export.Record) error {
 		before := buf.Len()
 
-		if err := e.formatMetric(rec, buf); err != nil && aggErr == nil {
-			aggErr = err
-			return
+		if err := e.formatMetric(rec, buf); err != nil {
+			return err
 		}
 
 		if buf.Len() < e.config.MaxPacketSize {
-			return
+			return nil
 		}
 		if before == 0 {
 			// A single metric >= packet size
@@ -180,7 +179,7 @@ func (e *Exporter) Export(_ context.Context, checkpointSet export.CheckpointSet)
 				sendErr = err
 			}
 			buf.Reset()
-			return
+			return nil
 		}
 
 		// Send and copy the leftover
@@ -193,6 +192,7 @@ func (e *Exporter) Export(_ context.Context, checkpointSet export.CheckpointSet)
 		copy(buf.Bytes()[0:leftover], buf.Bytes()[before:])
 
 		buf.Truncate(leftover)
+		return nil
 	})
 	if err := e.send(buf.Bytes()); err != nil && sendErr == nil {
 		sendErr = err
diff --git a/exporters/metric/prometheus/prometheus.go b/exporters/metric/prometheus/prometheus.go
index 133a58de387..3de10ee982e 100644
--- a/exporters/metric/prometheus/prometheus.go
+++ b/exporters/metric/prometheus/prometheus.go
@@ -184,8 +184,9 @@ func (c *collector) Describe(ch chan<- *prometheus.Desc) {
 		return
 	}
 
-	c.exp.snapshot.ForEach(func(record export.Record) {
+	_ = c.exp.snapshot.ForEach(func(record export.Record) error {
 		ch <- c.toDesc(&record)
+		return nil
 	})
 }
 
@@ -198,7 +199,7 @@ func (c *collector) Collect(ch chan<- prometheus.Metric) {
 		return
 	}
 
-	c.exp.snapshot.ForEach(func(record export.Record) {
+	_ = c.exp.snapshot.ForEach(func(record export.Record) error {
 		agg := record.Aggregator()
 		numberKind := record.Descriptor().NumberKind()
 		labels := labelValues(record.Labels())
@@ -222,6 +223,7 @@ func (c *collector) Collect(ch chan<- prometheus.Metric) {
 		} else if lastValue, ok := agg.(aggregator.LastValue); ok {
 			c.exportLastValue(ch, lastValue, numberKind, desc, labels)
 		}
+		return nil
 	})
 }
 
diff --git a/exporters/metric/stdout/stdout.go b/exporters/metric/stdout/stdout.go
index 465afdf7529..65838050d8d 100644
--- a/exporters/metric/stdout/stdout.go
+++ b/exporters/metric/stdout/stdout.go
@@ -139,15 +139,13 @@ func NewExportPipeline(config Config, period time.Duration) (*push.Controller, e
 }
 
 func (e *Exporter) Export(_ context.Context, checkpointSet export.CheckpointSet) error {
-	// N.B. Only return one aggError, if any occur. They're likely
-	// to be duplicates of the same error.
 	var aggError error
 	var batch expoBatch
 	if !e.config.DoNotPrintTime {
 		ts := time.Now()
 		batch.Timestamp = &ts
 	}
-	checkpointSet.ForEach(func(record export.Record) {
+	aggError = checkpointSet.ForEach(func(record export.Record) error {
 		desc := record.Descriptor()
 		agg := record.Aggregator()
 		kind := desc.NumberKind()
@@ -155,47 +153,31 @@ func (e *Exporter) Export(_ context.Context, checkpointSet export.CheckpointSet)
 		var expose expoLine
 
 		if sum, ok := agg.(aggregator.Sum); ok {
-			if value, err := sum.Sum(); err != nil {
-				aggError = err
-				expose.Sum = "NaN"
-			} else {
-				expose.Sum = value.AsInterface(kind)
+			value, err := sum.Sum()
+			if err != nil {
+				return err
 			}
+			expose.Sum = value.AsInterface(kind)
 		}
 
 		if mmsc, ok := agg.(aggregator.MinMaxSumCount); ok {
-			if count, err := mmsc.Count(); err != nil {
-				aggError = err
-				expose.Count = "NaN"
-			} else {
-				expose.Count = count
+			count, err := mmsc.Count()
+			if err != nil {
+				return err
 			}
+			expose.Count = count
 
-			if max, err := mmsc.Max(); err != nil {
-				if err == aggregator.ErrEmptyDataSet {
-					// This is a special case, indicates an aggregator that
-					// was checkpointed before its first value was set.
-					return
-				}
-
-				aggError = err
-				expose.Max = "NaN"
-			} else {
-				expose.Max = max.AsInterface(kind)
+			max, err := mmsc.Max()
+			if err != nil {
+				return err
 			}
+			expose.Max = max.AsInterface(kind)
 
-			if min, err := mmsc.Min(); err != nil {
-				if err == aggregator.ErrEmptyDataSet {
-					// This is a special case, indicates an aggregator that
-					// was checkpointed before its first value was set.
-					return
-				}
-
-				aggError = err
-				expose.Min = "NaN"
-			} else {
-				expose.Min = min.AsInterface(kind)
+			min, err := mmsc.Min()
+			if err != nil {
+				return err
 			}
+			expose.Min = min.AsInterface(kind)
 
 			if dist, ok := agg.(aggregator.Distribution); ok && len(e.config.Quantiles) != 0 {
 				summary := make([]expoQuantile, len(e.config.Quantiles))
@@ -203,12 +185,11 @@ func (e *Exporter) Export(_ context.Context, checkpointSet export.CheckpointSet)
 
 				for i, q := range e.config.Quantiles {
 					var vstr interface{}
-					if value, err := dist.Quantile(q); err != nil {
-						aggError = err
-						vstr = "NaN"
-					} else {
-						vstr = value.AsInterface(kind)
+					value, err := dist.Quantile(q)
+					if err != nil {
+						return err
 					}
+					vstr = value.AsInterface(kind)
 					summary[i] = expoQuantile{
 						Q: q,
 						V: vstr,
@@ -216,21 +197,14 @@ func (e *Exporter) Export(_ context.Context, checkpointSet export.CheckpointSet)
 				}
 			}
 		} else if lv, ok := agg.(aggregator.LastValue); ok {
-			if value, timestamp, err := lv.LastValue(); err != nil {
-				if err == aggregator.ErrNoLastValue {
-					// This is a special case, indicates an aggregator that
-					// was checkpointed before its first value was set.
-					return
-				}
-
-				aggError = err
-				expose.LastValue = "NaN"
-			} else {
-				expose.LastValue = value.AsInterface(kind)
+			value, timestamp, err := lv.LastValue()
+			if err != nil {
+				return err
+			}
+			expose.LastValue = value.AsInterface(kind)
 
-				if !e.config.DoNotPrintTime {
-					expose.Timestamp = &timestamp
-				}
+			if !e.config.DoNotPrintTime {
+				expose.Timestamp = &timestamp
 			}
 		}
 
@@ -264,6 +238,7 @@ func (e *Exporter) Export(_ context.Context, checkpointSet export.CheckpointSet)
 		expose.Name = sb.String()
 
 		batch.Updates = append(batch.Updates, expose)
+		return nil
 	})
 
 	var data []byte
diff --git a/exporters/metric/stdout/stdout_test.go b/exporters/metric/stdout/stdout_test.go
index d9c6544b0d4..eb8d0b1c28a 100644
--- a/exporters/metric/stdout/stdout_test.go
+++ b/exporters/metric/stdout/stdout_test.go
@@ -221,7 +221,7 @@ func TestStdoutMeasureFormat(t *testing.T) {
 }`, fix.Output())
 }
 
-func TestStdoutEmptyDataSet(t *testing.T) {
+func TestStdoutNoData(t *testing.T) {
 	desc := export.NewDescriptor("test.name", export.MeasureKind, nil, "", "", core.Float64NumberKind)
 	for name, tc := range map[string]export.Aggregator{
 		"ddsketch":       ddsketch.New(ddsketch.NewDefaultConfig(), desc),
diff --git a/exporters/metric/test/test.go b/exporters/metric/test/test.go
index 89172e8982b..71b97af051b 100644
--- a/exporters/metric/test/test.go
+++ b/exporters/metric/test/test.go
@@ -2,9 +2,11 @@ package test
 
 import (
 	"context"
+	"errors"
 
 	"go.opentelemetry.io/otel/api/core"
 	export "go.opentelemetry.io/otel/sdk/export/metric"
+	"go.opentelemetry.io/otel/sdk/export/metric/aggregator"
 	"go.opentelemetry.io/otel/sdk/metric/aggregator/array"
 	"go.opentelemetry.io/otel/sdk/metric/aggregator/lastvalue"
 	"go.opentelemetry.io/otel/sdk/metric/aggregator/sum"
@@ -82,8 +84,11 @@ func (p *CheckpointSet) updateAggregator(desc *export.Descriptor, newAgg export.
 	}
 }
 
-func (p *CheckpointSet) ForEach(f func(export.Record)) {
+func (p *CheckpointSet) ForEach(f func(export.Record) error) error {
 	for _, r := range p.updates {
-		f(r)
+		if err := f(r); err != nil && !errors.Is(err, aggregator.ErrNoData) {
+			return err
+		}
 	}
+	return nil
 }
diff --git a/exporters/otlp/internal/transform/metric_test.go b/exporters/otlp/internal/transform/metric_test.go
index b8eb613363b..7f337bb5358 100644
--- a/exporters/otlp/internal/transform/metric_test.go
+++ b/exporters/otlp/internal/transform/metric_test.go
@@ -77,9 +77,9 @@ func TestMinMaxSumCountValue(t *testing.T) {
 	assert.NoError(t, mmsc.Update(context.Background(), 1, &metricsdk.Descriptor{}))
 	assert.NoError(t, mmsc.Update(context.Background(), 10, &metricsdk.Descriptor{}))
 
-	// Prior to checkpointing ErrEmptyDataSet should be returned.
+	// Prior to checkpointing ErrNoData should be returned.
 	_, _, _, _, err := minMaxSumCountValues(mmsc)
-	assert.Error(t, err, aggregator.ErrEmptyDataSet)
+	assert.EqualError(t, err, aggregator.ErrNoData.Error())
 
 	// Checkpoint to set non-zero values
 	mmsc.Checkpoint(context.Background(), &metricsdk.Descriptor{})
@@ -186,13 +186,13 @@ func TestMinMaxSumCountDatapoints(t *testing.T) {
 }
 
 func TestMinMaxSumCountPropagatesErrors(t *testing.T) {
-	// ErrEmptyDataSet should be returned by both the Min and Max values of
+	// ErrNoData should be returned by both the Min and Max values of
 	// a MinMaxSumCount Aggregator. Use this fact to check the error is
 	// correctly returned.
 	mmsc := minmaxsumcount.New(&metricsdk.Descriptor{})
 	_, _, _, _, err := minMaxSumCountValues(mmsc)
 	assert.Error(t, err)
-	assert.Equal(t, aggregator.ErrEmptyDataSet, err)
+	assert.Equal(t, aggregator.ErrNoData, err)
 }
 
 func TestSumMetricDescriptor(t *testing.T) {
diff --git a/exporters/otlp/otlp.go b/exporters/otlp/otlp.go
index 4e9d99320ac..352f03baddb 100644
--- a/exporters/otlp/otlp.go
+++ b/exporters/otlp/otlp.go
@@ -217,12 +217,13 @@ func (e *Exporter) Export(ctx context.Context, cps metricsdk.CheckpointSet) erro
 	// Seed records into the work processing pool.
 	records := make(chan metricsdk.Record)
 	go func() {
-		cps.ForEach(func(record metricsdk.Record) {
+		_ = cps.ForEach(func(record metricsdk.Record) (err error) {
 			select {
 			case <-e.stopCh:
 			case <-ctx.Done():
 			case records <- record:
 			}
+			return
 		})
 		close(records)
 	}()
@@ -268,7 +269,7 @@ func (e *Exporter) processMetrics(ctx context.Context, out chan<- *metricpb.Metr
 	for r := range in {
 		m, err := transform.Record(r)
 		if err != nil {
-			if err == aggregator.ErrEmptyDataSet {
+			if err == aggregator.ErrNoData {
 				// The Aggregator was checkpointed before the first value
 				// was set, skipping.
 				continue
diff --git a/sdk/export/metric/aggregator/aggregator.go b/sdk/export/metric/aggregator/aggregator.go
index 27766d59666..2b738c575f1 100644
--- a/sdk/export/metric/aggregator/aggregator.go
+++ b/sdk/export/metric/aggregator/aggregator.go
@@ -97,20 +97,12 @@ var (
 	ErrInvalidQuantile  = fmt.Errorf("the requested quantile is out of range")
 	ErrNegativeInput    = fmt.Errorf("negative value is out of range for this instrument")
 	ErrNaNInput         = fmt.Errorf("NaN value is an invalid input")
-	ErrNonMonotoneInput = fmt.Errorf("the new value is not monotone")
 	ErrInconsistentType = fmt.Errorf("inconsistent aggregator types")
 
-	// ErrNoLastValue is returned by the LastValue interface when
-	// (due to a race with collection) the Aggregator is
-	// checkpointed before the first value is set.  The aggregator
-	// should simply be skipped in this case.
-	ErrNoLastValue = fmt.Errorf("no value has been set")
-
-	// ErrEmptyDataSet is returned by Max and Quantile interfaces
-	// when (due to a race with collection) the Aggregator is
-	// checkpointed before the first value is set.  The aggregator
-	// should simply be skipped in this case.
-	ErrEmptyDataSet = fmt.Errorf("the result is not defined on an empty data set")
+	// ErrNoData is returned when (due to a race with collection)
+	// the Aggregator is check-pointed before the first value is set.
+	// The aggregator should simply be skipped in this case.
+	ErrNoData = fmt.Errorf("no data collected by this aggregator")
 )
 
 // NewInconsistentMergeError formats an error describing an attempt to
diff --git a/sdk/export/metric/metric.go b/sdk/export/metric/metric.go
index dd5adae8d45..a626950b0f4 100644
--- a/sdk/export/metric/metric.go
+++ b/sdk/export/metric/metric.go
@@ -201,8 +201,13 @@ type LabelEncoder interface {
 type CheckpointSet interface {
 	// ForEach iterates over aggregated checkpoints for all
 	// metrics that were updated during the last collection
-	// period.
-	ForEach(func(Record))
+	// period. Each aggregated checkpoint returned by the
+	// function parameter may return an error.
+	// ForEach tolerates ErrNoData silently, as this is
+	// expected from the Meter implementation. Any other kind
+	// of error will immediately halt ForEach and return
+	// the error to the caller.
+	ForEach(func(Record) error) error
 }
 
 // Record contains the exported data for a single metric instrument
diff --git a/sdk/metric/aggregator/array/array.go b/sdk/metric/aggregator/array/array.go
index 3855e8cc28c..ea8d1a8cd84 100644
--- a/sdk/metric/aggregator/array/array.go
+++ b/sdk/metric/aggregator/array/array.go
@@ -177,7 +177,7 @@ func (p *points) Swap(i, j int) {
 // of a quantile.
 func (p *points) Quantile(q float64) (core.Number, error) {
 	if len(*p) == 0 {
-		return core.Number(0), aggregator.ErrEmptyDataSet
+		return core.Number(0), aggregator.ErrNoData
 	}
 
 	if q < 0 || q > 1 {
diff --git a/sdk/metric/aggregator/array/array_test.go b/sdk/metric/aggregator/array/array_test.go
index a7ff5fcd5ca..7bf3b2f4b5e 100644
--- a/sdk/metric/aggregator/array/array_test.go
+++ b/sdk/metric/aggregator/array/array_test.go
@@ -204,15 +204,15 @@ func TestArrayErrors(t *testing.T) {
 
 		_, err := agg.Max()
 		require.Error(t, err)
-		require.Equal(t, err, aggregator.ErrEmptyDataSet)
+		require.Equal(t, err, aggregator.ErrNoData)
 
 		_, err = agg.Min()
 		require.Error(t, err)
-		require.Equal(t, err, aggregator.ErrEmptyDataSet)
+		require.Equal(t, err, aggregator.ErrNoData)
 
 		_, err = agg.Quantile(0.1)
 		require.Error(t, err)
-		require.Equal(t, err, aggregator.ErrEmptyDataSet)
+		require.Equal(t, err, aggregator.ErrNoData)
 
 		ctx := context.Background()
 
diff --git a/sdk/metric/aggregator/ddsketch/ddsketch.go b/sdk/metric/aggregator/ddsketch/ddsketch.go
index 324edca7c93..7af36f835ea 100644
--- a/sdk/metric/aggregator/ddsketch/ddsketch.go
+++ b/sdk/metric/aggregator/ddsketch/ddsketch.go
@@ -85,7 +85,7 @@ func (c *Aggregator) Min() (core.Number, error) {
 // It is an error if `q` is less than 0 or greated than 1.
 func (c *Aggregator) Quantile(q float64) (core.Number, error) {
 	if c.checkpoint.Count() == 0 {
-		return core.Number(0), aggregator.ErrEmptyDataSet
+		return core.Number(0), aggregator.ErrNoData
 	}
 	f := c.checkpoint.Quantile(q)
 	if math.IsNaN(f) {
diff --git a/sdk/metric/aggregator/lastvalue/lastvalue.go b/sdk/metric/aggregator/lastvalue/lastvalue.go
index f1997537bd7..f7bf76ce931 100644
--- a/sdk/metric/aggregator/lastvalue/lastvalue.go
+++ b/sdk/metric/aggregator/lastvalue/lastvalue.go
@@ -68,13 +68,13 @@ func New() *Aggregator {
 }
 
 // LastValue returns the last-recorded lastValue value and the
-// corresponding timestamp.  The error value aggregator.ErrNoLastValue
+// corresponding timestamp.  The error value aggregator.ErrNoData
 // will be returned if (due to a race condition) the checkpoint was
 // computed before the first value was set.
 func (g *Aggregator) LastValue() (core.Number, time.Time, error) {
 	gd := (*lastValueData)(g.checkpoint)
 	if gd == unsetLastValue {
-		return core.Number(0), time.Time{}, aggregator.ErrNoLastValue
+		return core.Number(0), time.Time{}, aggregator.ErrNoData
 	}
 	return gd.value.AsNumber(), gd.timestamp, nil
 }
diff --git a/sdk/metric/aggregator/lastvalue/lastvalue_test.go b/sdk/metric/aggregator/lastvalue/lastvalue_test.go
index 7705e48b6ca..300c03b2c52 100644
--- a/sdk/metric/aggregator/lastvalue/lastvalue_test.go
+++ b/sdk/metric/aggregator/lastvalue/lastvalue_test.go
@@ -113,7 +113,7 @@ func TestLastValueNotSet(t *testing.T) {
 	g.Checkpoint(context.Background(), descriptor)
 
 	value, timestamp, err := g.LastValue()
-	require.Equal(t, aggregator.ErrNoLastValue, err)
+	require.Equal(t, aggregator.ErrNoData, err)
 	require.True(t, timestamp.IsZero())
 	require.Equal(t, core.Number(0), value)
 }
diff --git a/sdk/metric/aggregator/minmaxsumcount/mmsc.go b/sdk/metric/aggregator/minmaxsumcount/mmsc.go
index bbd7a2bccd5..75372c57765 100644
--- a/sdk/metric/aggregator/minmaxsumcount/mmsc.go
+++ b/sdk/metric/aggregator/minmaxsumcount/mmsc.go
@@ -86,25 +86,25 @@ func (c *Aggregator) Count() (int64, error) {
 }
 
 // Min returns the minimum value in the checkpoint.
-// The error value aggregator.ErrEmptyDataSet will be returned
+// The error value aggregator.ErrNoData will be returned
 // if there were no measurements recorded during the checkpoint.
 func (c *Aggregator) Min() (core.Number, error) {
 	c.lock.Lock()
 	defer c.lock.Unlock()
 	if c.checkpoint().count.IsZero(core.Uint64NumberKind) {
-		return c.kind.Zero(), aggregator.ErrEmptyDataSet
+		return c.kind.Zero(), aggregator.ErrNoData
 	}
 	return c.checkpoint().min, nil
 }
 
 // Max returns the maximum value in the checkpoint.
-// The error value aggregator.ErrEmptyDataSet will be returned
+// The error value aggregator.ErrNoData will be returned
 // if there were no measurements recorded during the checkpoint.
 func (c *Aggregator) Max() (core.Number, error) {
 	c.lock.Lock()
 	defer c.lock.Unlock()
 	if c.checkpoint().count.IsZero(core.Uint64NumberKind) {
-		return c.kind.Zero(), aggregator.ErrEmptyDataSet
+		return c.kind.Zero(), aggregator.ErrNoData
 	}
 	return c.checkpoint().max, nil
 }
diff --git a/sdk/metric/aggregator/minmaxsumcount/mmsc_test.go b/sdk/metric/aggregator/minmaxsumcount/mmsc_test.go
index 5b365890297..8b6a8f24876 100644
--- a/sdk/metric/aggregator/minmaxsumcount/mmsc_test.go
+++ b/sdk/metric/aggregator/minmaxsumcount/mmsc_test.go
@@ -234,7 +234,7 @@ func TestMaxSumCountNotSet(t *testing.T) {
 		require.Nil(t, err)
 
 		max, err := agg.Max()
-		require.Equal(t, aggregator.ErrEmptyDataSet, err)
+		require.Equal(t, aggregator.ErrNoData, err)
 		require.Equal(t, core.Number(0), max)
 	})
 }
diff --git a/sdk/metric/batcher/defaultkeys/defaultkeys.go b/sdk/metric/batcher/defaultkeys/defaultkeys.go
index 4b0a36ebb27..57757df0874 100644
--- a/sdk/metric/batcher/defaultkeys/defaultkeys.go
+++ b/sdk/metric/batcher/defaultkeys/defaultkeys.go
@@ -16,9 +16,11 @@ package defaultkeys // import "go.opentelemetry.io/otel/sdk/metric/batcher/defau
 
 import (
 	"context"
+	"errors"
 
 	"go.opentelemetry.io/otel/api/core"
 	export "go.opentelemetry.io/otel/sdk/export/metric"
+	"go.opentelemetry.io/otel/sdk/export/metric/aggregator"
 )
 
 type (
@@ -153,8 +155,11 @@ func (b *Batcher) FinishedCollection() {
 	}
 }
 
-func (p *checkpointSet) ForEach(f func(export.Record)) {
+func (p *checkpointSet) ForEach(f func(export.Record) error) error {
 	for _, entry := range p.aggCheckpointMap {
-		f(entry)
+		if err := f(entry); err != nil && !errors.Is(err, aggregator.ErrNoData) {
+			return err
+		}
 	}
+	return nil
 }
diff --git a/sdk/metric/batcher/defaultkeys/defaultkeys_test.go b/sdk/metric/batcher/defaultkeys/defaultkeys_test.go
index 0a5974daced..8509c18c3ff 100644
--- a/sdk/metric/batcher/defaultkeys/defaultkeys_test.go
+++ b/sdk/metric/batcher/defaultkeys/defaultkeys_test.go
@@ -50,7 +50,8 @@ func TestGroupingStateless(t *testing.T) {
 	b.FinishedCollection()
 
 	records := test.Output{}
-	checkpointSet.ForEach(records.AddTo)
+	err := checkpointSet.ForEach(records.AddTo)
+	require.NoError(t, err)
 
 	// Repeat for {counter,lastvalue}.{1,2}.
 	// Output lastvalue should have only the "G=H" and "G=" keys.
@@ -69,8 +70,9 @@ func TestGroupingStateless(t *testing.T) {
 	// Verify that state is reset by FinishedCollection()
 	checkpointSet = b.CheckpointSet()
 	b.FinishedCollection()
-	checkpointSet.ForEach(func(rec export.Record) {
+	_ = checkpointSet.ForEach(func(rec export.Record) error {
 		t.Fatal("Unexpected call")
+		return nil
 	})
 }
 
@@ -90,7 +92,8 @@ func TestGroupingStateful(t *testing.T) {
 	b.FinishedCollection()
 
 	records1 := test.Output{}
-	checkpointSet.ForEach(records1.AddTo)
+	err := checkpointSet.ForEach(records1.AddTo)
+	require.NoError(t, err)
 
 	require.EqualValues(t, map[string]int64{
 		"sum.a/C=D": 10, // labels1
@@ -102,7 +105,8 @@ func TestGroupingStateful(t *testing.T) {
 	b.FinishedCollection()
 
 	records2 := test.Output{}
-	checkpointSet.ForEach(records2.AddTo)
+	err = checkpointSet.ForEach(records2.AddTo)
+	require.NoError(t, err)
 
 	require.EqualValues(t, records1, records2)
 
@@ -118,7 +122,8 @@ func TestGroupingStateful(t *testing.T) {
 	b.FinishedCollection()
 
 	records3 := test.Output{}
-	checkpointSet.ForEach(records3.AddTo)
+	err = checkpointSet.ForEach(records3.AddTo)
+	require.NoError(t, err)
 
 	require.EqualValues(t, records1, records3)
 
@@ -130,7 +135,8 @@ func TestGroupingStateful(t *testing.T) {
 	b.FinishedCollection()
 
 	records4 := test.Output{}
-	checkpointSet.ForEach(records4.AddTo)
+	err = checkpointSet.ForEach(records4.AddTo)
+	require.NoError(t, err)
 
 	require.EqualValues(t, map[string]int64{
 		"sum.a/C=D": 30,
diff --git a/sdk/metric/batcher/test/test.go b/sdk/metric/batcher/test/test.go
index 4a791f1a8b6..539954a2f91 100644
--- a/sdk/metric/batcher/test/test.go
+++ b/sdk/metric/batcher/test/test.go
@@ -134,7 +134,7 @@ func CounterAgg(desc *export.Descriptor, v int64) export.Aggregator {
 
 // AddTo adds a name/label-encoding entry with the lastValue or counter
 // value to the output map.
-func (o Output) AddTo(rec export.Record) {
+func (o Output) AddTo(rec export.Record) error {
 	labels := rec.Labels()
 	key := fmt.Sprint(rec.Descriptor().Name(), "/", labels.Encoded())
 	var value int64
@@ -147,4 +147,5 @@ func (o Output) AddTo(rec export.Record) {
 		value = lv.AsInt64()
 	}
 	o[key] = value
+	return nil
 }
diff --git a/sdk/metric/batcher/ungrouped/ungrouped.go b/sdk/metric/batcher/ungrouped/ungrouped.go
index 76f53fc2bb7..6e098f73146 100644
--- a/sdk/metric/batcher/ungrouped/ungrouped.go
+++ b/sdk/metric/batcher/ungrouped/ungrouped.go
@@ -16,8 +16,10 @@ package ungrouped // import "go.opentelemetry.io/otel/sdk/metric/batcher/ungroup
 
 import (
 	"context"
+	"errors"
 
 	export "go.opentelemetry.io/otel/sdk/export/metric"
+	"go.opentelemetry.io/otel/sdk/export/metric/aggregator"
 )
 
 type (
@@ -101,12 +103,15 @@ func (b *Batcher) FinishedCollection() {
 	}
 }
 
-func (c batchMap) ForEach(f func(export.Record)) {
+func (c batchMap) ForEach(f func(export.Record) error) error {
 	for key, value := range c {
-		f(export.NewRecord(
+		if err := f(export.NewRecord(
 			key.descriptor,
 			value.labels,
 			value.aggregator,
-		))
+		)); err != nil && !errors.Is(err, aggregator.ErrNoData) {
+			return err
+		}
 	}
+	return nil
 }
diff --git a/sdk/metric/batcher/ungrouped/ungrouped_test.go b/sdk/metric/batcher/ungrouped/ungrouped_test.go
index efde762e7b1..6e9392cf57e 100644
--- a/sdk/metric/batcher/ungrouped/ungrouped_test.go
+++ b/sdk/metric/batcher/ungrouped/ungrouped_test.go
@@ -62,7 +62,7 @@ func TestUngroupedStateless(t *testing.T) {
 	b.FinishedCollection()
 
 	records := test.Output{}
-	checkpointSet.ForEach(records.AddTo)
+	_ = checkpointSet.ForEach(records.AddTo)
 
 	// Output lastvalue should have only the "G=H" and "G=" keys.
 	// Output counter should have only the "C=D" and "C=" keys.
@@ -84,8 +84,9 @@ func TestUngroupedStateless(t *testing.T) {
 	// Verify that state was reset
 	checkpointSet = b.CheckpointSet()
 	b.FinishedCollection()
-	checkpointSet.ForEach(func(rec export.Record) {
+	_ = checkpointSet.ForEach(func(rec export.Record) error {
 		t.Fatal("Unexpected call")
+		return nil
 	})
 }
 
@@ -105,7 +106,7 @@ func TestUngroupedStateful(t *testing.T) {
 	b.FinishedCollection()
 
 	records1 := test.Output{}
-	checkpointSet.ForEach(records1.AddTo)
+	_ = checkpointSet.ForEach(records1.AddTo)
 
 	require.EqualValues(t, map[string]int64{
 		"sum.a/G~H&C~D": 10, // labels1
@@ -117,7 +118,7 @@ func TestUngroupedStateful(t *testing.T) {
 	b.FinishedCollection()
 
 	records2 := test.Output{}
-	checkpointSet.ForEach(records2.AddTo)
+	_ = checkpointSet.ForEach(records2.AddTo)
 
 	require.EqualValues(t, records1, records2)
 
@@ -133,7 +134,7 @@ func TestUngroupedStateful(t *testing.T) {
 	b.FinishedCollection()
 
 	records3 := test.Output{}
-	checkpointSet.ForEach(records3.AddTo)
+	_ = checkpointSet.ForEach(records3.AddTo)
 
 	require.EqualValues(t, records1, records3)
 
@@ -145,7 +146,7 @@ func TestUngroupedStateful(t *testing.T) {
 	b.FinishedCollection()
 
 	records4 := test.Output{}
-	checkpointSet.ForEach(records4.AddTo)
+	_ = checkpointSet.ForEach(records4.AddTo)
 
 	require.EqualValues(t, map[string]int64{
 		"sum.a/G~H&C~D": 30,
diff --git a/sdk/metric/controller/push/push.go b/sdk/metric/controller/push/push.go
index cb2294a1c74..22bcc2c5575 100644
--- a/sdk/metric/controller/push/push.go
+++ b/sdk/metric/controller/push/push.go
@@ -190,10 +190,10 @@ type syncCheckpointSet struct {
 
 var _ export.CheckpointSet = (*syncCheckpointSet)(nil)
 
-func (c syncCheckpointSet) ForEach(fn func(export.Record)) {
+func (c syncCheckpointSet) ForEach(fn func(export.Record) error) error {
 	c.mtx.Lock()
 	defer c.mtx.Unlock()
-	c.delegate.ForEach(fn)
+	return c.delegate.ForEach(fn)
 }
 
 func (realClock) Now() time.Time {
diff --git a/sdk/metric/controller/push/push_test.go b/sdk/metric/controller/push/push_test.go
index 82b725b7465..6ecf57a4c21 100644
--- a/sdk/metric/controller/push/push_test.go
+++ b/sdk/metric/controller/push/push_test.go
@@ -43,11 +43,11 @@ type testBatcher struct {
 }
 
 type testExporter struct {
-	t       *testing.T
-	lock    sync.Mutex
-	exports int
-	records []export.Record
-	retErr  error
+	t         *testing.T
+	lock      sync.Mutex
+	exports   int
+	records   []export.Record
+	injectErr func(r export.Record) error
 }
 
 type testFixture struct {
@@ -118,10 +118,20 @@ func (e *testExporter) Export(_ context.Context, checkpointSet export.Checkpoint
 	e.lock.Lock()
 	defer e.lock.Unlock()
 	e.exports++
-	checkpointSet.ForEach(func(r export.Record) {
-		e.records = append(e.records, r)
-	})
-	return e.retErr
+	var records []export.Record
+	if err := checkpointSet.ForEach(func(r export.Record) error {
+		if e.injectErr != nil {
+			if err := e.injectErr(r); err != nil {
+				return err
+			}
+		}
+		records = append(records, r)
+		return nil
+	}); err != nil {
+		return err
+	}
+	e.records = records
+	return nil
 }
 
 func (e *testExporter) resetRecords() ([]export.Record, int) {
@@ -230,37 +240,81 @@ func TestPushTicker(t *testing.T) {
 }
 
 func TestPushExportError(t *testing.T) {
-	fix := newFixture(t)
-	fix.exporter.retErr = fmt.Errorf("test export error")
-
-	p := push.New(fix.batcher, fix.exporter, time.Second)
-
-	var err error
-	var lock sync.Mutex
-	p.SetErrorHandler(func(sdkErr error) {
-		lock.Lock()
-		defer lock.Unlock()
-		err = sdkErr
-	})
-
-	mock := mockClock{clock.NewMock()}
-	p.SetClock(mock)
-
-	p.Start()
-	runtime.Gosched()
-
-	require.Equal(t, 0, fix.exporter.exports)
-	require.Nil(t, err)
-
-	mock.Add(time.Second)
-	runtime.Gosched()
-
-	lock.Lock()
-	_, exports := fix.batcher.getCounts()
-	require.Equal(t, 1, exports)
-	require.Error(t, err)
-	require.Equal(t, fix.exporter.retErr, err)
-	lock.Unlock()
-
-	p.Stop()
+	injector := func(name string, e error) func(r export.Record) error {
+		return func(r export.Record) error {
+			if r.Descriptor().Name() == name {
+				return e
+			}
+			return nil
+		}
+	}
+	var errAggregator = fmt.Errorf("unexpected error")
+	var tests = []struct {
+		name                string
+		injectedError       error
+		expectedDescriptors []string
+		expectedError       error
+	}{
+		{"errNone", nil, []string{"counter1", "counter2"}, nil},
+		{"errNoData", aggregator.ErrNoData, []string{"counter2"}, nil},
+		{"errUnexpected", errAggregator, []string{}, errAggregator},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			fix := newFixture(t)
+			fix.exporter.injectErr = injector("counter1", tt.injectedError)
+
+			p := push.New(fix.batcher, fix.exporter, time.Second)
+
+			var err error
+			var lock sync.Mutex
+			p.SetErrorHandler(func(sdkErr error) {
+				lock.Lock()
+				defer lock.Unlock()
+				err = sdkErr
+			})
+
+			mock := mockClock{clock.NewMock()}
+			p.SetClock(mock)
+
+			ctx := context.Background()
+
+			meter := p.Meter("name")
+			counter1 := metric.Must(meter).NewInt64Counter("counter1")
+			counter2 := metric.Must(meter).NewInt64Counter("counter2")
+
+			p.Start()
+			runtime.Gosched()
+
+			counter1.Add(ctx, 3, meter.Labels())
+			counter2.Add(ctx, 5, meter.Labels())
+
+			require.Equal(t, 0, fix.exporter.exports)
+			require.Nil(t, err)
+
+			mock.Add(time.Second)
+			runtime.Gosched()
+
+			records, exports := fix.exporter.resetRecords()
+			checkpoints, finishes := fix.batcher.getCounts()
+			require.Equal(t, 1, exports)
+			require.Equal(t, 1, checkpoints)
+			require.Equal(t, 1, finishes)
+			lock.Lock()
+			if tt.expectedError == nil {
+				require.NoError(t, err)
+			} else {
+				require.Error(t, err)
+				require.Equal(t, tt.expectedError, err)
+			}
+			lock.Unlock()
+			require.Equal(t, len(tt.expectedDescriptors), len(records))
+			for _, r := range records {
+				require.Contains(t, tt.expectedDescriptors, r.Descriptor().Name())
+			}
+
+			p.Stop()
+
+		})
+	}
 }
diff --git a/sdk/metric/stress_test.go b/sdk/metric/stress_test.go
index d00727c6c8c..fd44dfabb79 100644
--- a/sdk/metric/stress_test.go
+++ b/sdk/metric/stress_test.go
@@ -272,7 +272,7 @@ func (f *testFixture) Process(_ context.Context, record export.Record) error {
 		f.impl.storeCollect(actual, sum, time.Time{})
 	case export.MeasureKind:
 		lv, ts, err := agg.(aggregator.LastValue).LastValue()
-		if err != nil && err != aggregator.ErrNoLastValue {
+		if err != nil && err != aggregator.ErrNoData {
 			f.T.Fatal("Last value error: ", err)
 		}
 		f.impl.storeCollect(actual, lv, ts)