diff --git a/IntegrationTests/tests_01_allocation_counters/test_01_allocation_counts.sh b/IntegrationTests/tests_01_allocation_counters/test_01_allocation_counts.sh
index 74a823ca..080b8255 100644
--- a/IntegrationTests/tests_01_allocation_counters/test_01_allocation_counts.sh
+++ b/IntegrationTests/tests_01_allocation_counters/test_01_allocation_counts.sh
@@ -30,23 +30,28 @@ done
 
 for test in "${all_tests[@]}"; do
     cat "$tmp/output"  # helps debugging
-    total_allocations=$(grep "^test_$test.total_allocations:" "$tmp/output" | cut -d: -f2 | sed 's/ //g')
-    not_freed_allocations=$(grep "^test_$test.remaining_allocations:" "$tmp/output" | cut -d: -f2 | sed 's/ //g')
-    max_allowed_env_name="MAX_ALLOCS_ALLOWED_$test"
 
-    info "$test: allocations not freed: $not_freed_allocations"
-    info "$test: total number of mallocs: $total_allocations"
+    while read -r test_case; do
+        test_case=${test_case#test_*}
+        total_allocations=$(grep "^test_$test_case.total_allocations:" "$tmp/output" | cut -d: -f2 | sed 's/ //g')
+        not_freed_allocations=$(grep "^test_$test_case.remaining_allocations:" "$tmp/output" | cut -d: -f2 | sed 's/ //g')
+        max_allowed_env_name="MAX_ALLOCS_ALLOWED_$test_case"
 
-    assert_less_than "$not_freed_allocations" 5     # allow some slack
-    assert_greater_than "$not_freed_allocations" -5 # allow some slack
-    assert_greater_than "$total_allocations" 1000
-    if [[ -z "${!max_allowed_env_name+x}" ]]; then
+        info "$test_case: allocations not freed: $not_freed_allocations"
+        info "$test_case: total number of mallocs: $total_allocations"
+
+        assert_less_than "$not_freed_allocations" 5     # allow some slack
+        assert_greater_than "$not_freed_allocations" -5 # allow some slack
         if [[ -z "${!max_allowed_env_name+x}" ]]; then
-            warn "no reference number of allocations set (set to \$$max_allowed_env_name)"
-            warn "to set current number:"
-            warn "    export $max_allowed_env_name=$total_allocations"
+            if [[ -z "${!max_allowed_env_name+x}" ]]; then
+                warn "no reference number of allocations set (set to \$$max_allowed_env_name)"
+                warn "to set current number:"
+                warn "    export $max_allowed_env_name=$total_allocations"
+            fi
+        else
+            max_allowed=${!max_allowed_env_name}
+            assert_less_than_or_equal "$total_allocations" "$max_allowed"
+            assert_greater_than "$total_allocations" "$(( max_allowed - 1000))"
         fi
-    else
-        assert_less_than_or_equal "$total_allocations" "${!max_allowed_env_name}"
-    fi
+    done < <(grep "^test_$test[^\W]*.total_allocations:" "$tmp/output" | cut -d: -f1 | cut -d. -f1 | sort | uniq)
 done
diff --git a/IntegrationTests/tests_01_allocation_counters/test_01_resources/run-nio-http2-alloc-counter-tests.sh b/IntegrationTests/tests_01_allocation_counters/test_01_resources/run-nio-http2-alloc-counter-tests.sh
index 15d85053..83c73040 100755
--- a/IntegrationTests/tests_01_allocation_counters/test_01_resources/run-nio-http2-alloc-counter-tests.sh
+++ b/IntegrationTests/tests_01_allocation_counters/test_01_resources/run-nio-http2-alloc-counter-tests.sh
@@ -18,18 +18,13 @@ here="$( cd "$( dirname "${BASH_SOURCE[0]}" )" && pwd )"
 
 tmp_dir="/tmp"
 
-function die() {
-    echo >&2 "ERROR: $*"
-    exit 1
-}
-
 while getopts "t:" opt; do
     case "$opt" in
         t)
             tmp_dir="$OPTARG"
             ;;
-        \?)
-            die "unknown option $opt"
+        *)
+            exit 1
             ;;
     esac
 done
@@ -40,6 +35,14 @@ cd "$nio_checkout"
 git clone --depth 1 https://github.com/apple/swift-nio
 )
 
+shift $((OPTIND-1))
+
+tests_to_run=("$here"/test_*.swift)
+
+if [[ $# -gt 0 ]]; then
+    tests_to_run=("$@")
+fi
+
 "$nio_checkout/swift-nio/IntegrationTests/allocation-counter-tests-framework/run-allocation-counter.sh" \
     -p "$here/../../.." \
     -m NIO \
@@ -47,4 +50,4 @@ git clone --depth 1 https://github.com/apple/swift-nio
     -m NIOHTTP2 \
     -t "$tmp_dir" \
     -d <( echo '.package(url: "https://github.com/apple/swift-nio.git", from: "2.0.0"),' ) \
-    "$here"/test_*.swift
+    "${tests_to_run[@]}"
diff --git a/docker/docker-compose.1604.51.yaml b/docker/docker-compose.1604.51.yaml
index ee8ab7ff..6a88b100 100644
--- a/docker/docker-compose.1604.51.yaml
+++ b/docker/docker-compose.1604.51.yaml
@@ -16,10 +16,10 @@ services:
   integration-tests:
     image: swift-nio-http2:16.04-5.1
     environment:
-      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=72010
+      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=63000
       - MAX_ALLOCS_ALLOWED_hpack_decoding=5050
-      - MAX_ALLOCS_ALLOWED_client_server_request_response=378000
-      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=409000
+      - MAX_ALLOCS_ALLOWED_client_server_request_response=338000
+      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=406000
 
   performance-test:
     image: swift-nio-http2:16.04-5.1
@@ -30,10 +30,10 @@ services:
   test:
     image: swift-nio-http2:16.04-5.1
     environment:
-      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=72010
+      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=63000
       - MAX_ALLOCS_ALLOWED_hpack_decoding=5050
-      - MAX_ALLOCS_ALLOWED_client_server_request_response=378000
-      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=409000
+      - MAX_ALLOCS_ALLOWED_client_server_request_response=338000
+      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=406000
       - SANITIZER_ARG=--sanitize=thread
 
   shell:
diff --git a/docker/docker-compose.1804.50.yaml b/docker/docker-compose.1804.50.yaml
index a88f0fa2..ee35ace9 100644
--- a/docker/docker-compose.1804.50.yaml
+++ b/docker/docker-compose.1804.50.yaml
@@ -16,9 +16,9 @@ services:
   integration-tests:
     image: swift-nio-http2:18.04-5.0
     environment:
-      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=72010
+      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=67000
       - MAX_ALLOCS_ALLOWED_hpack_decoding=5050
-      - MAX_ALLOCS_ALLOWED_client_server_request_response=384810
+      - MAX_ALLOCS_ALLOWED_client_server_request_response=358000
       - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=425000
 
   performance-test:
@@ -30,9 +30,9 @@ services:
   test:
     image: swift-nio-http2:18.04-5.0
     environment:
-      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=72010
+      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=67000
       - MAX_ALLOCS_ALLOWED_hpack_decoding=5050
-      - MAX_ALLOCS_ALLOWED_client_server_request_response=384810
+      - MAX_ALLOCS_ALLOWED_client_server_request_response=358000
       - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=425000
 
   shell:
diff --git a/docker/docker-compose.1804.52.yaml b/docker/docker-compose.1804.52.yaml
index cf6a78da..56846498 100644
--- a/docker/docker-compose.1804.52.yaml
+++ b/docker/docker-compose.1804.52.yaml
@@ -16,10 +16,10 @@ services:
   integration-tests:
     image: swift-nio-http2:18.04-5.2
     environment:
-      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=72010
+      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=63000
       - MAX_ALLOCS_ALLOWED_hpack_decoding=5050
-      - MAX_ALLOCS_ALLOWED_client_server_request_response=384810
-      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=409000
+      - MAX_ALLOCS_ALLOWED_client_server_request_response=334000
+      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=403000
 
   performance-test:
     image: swift-nio-http2:18.04-5.2
@@ -30,10 +30,10 @@ services:
   test:
     image: swift-nio-http2:18.04-5.2
     environment:
-      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=72010
+      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=63000
       - MAX_ALLOCS_ALLOWED_hpack_decoding=5050
-      - MAX_ALLOCS_ALLOWED_client_server_request_response=384810
-      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=409000
+      - MAX_ALLOCS_ALLOWED_client_server_request_response=334000
+      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=403000
 
 
   shell:
diff --git a/docker/docker-compose.1804.53.yaml b/docker/docker-compose.1804.53.yaml
index c1f6d4e7..7256e889 100644
--- a/docker/docker-compose.1804.53.yaml
+++ b/docker/docker-compose.1804.53.yaml
@@ -16,10 +16,10 @@ services:
   integration-tests:
     image: swift-nio-http2:18.04-5.3
     environment:
-      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=72010
+      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=63000
       - MAX_ALLOCS_ALLOWED_hpack_decoding=5050
-      - MAX_ALLOCS_ALLOWED_client_server_request_response=384810
-      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=409000
+      - MAX_ALLOCS_ALLOWED_client_server_request_response=334000
+      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=403000
 
   performance-test:
     image: swift-nio-http2:18.04-5.3
@@ -30,10 +30,10 @@ services:
   test:
     image: swift-nio-http2:18.04-5.3
     environment:
-      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=72010
+      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=63000
       - MAX_ALLOCS_ALLOWED_hpack_decoding=5050
-      - MAX_ALLOCS_ALLOWED_client_server_request_response=384810
-      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=409000
+      - MAX_ALLOCS_ALLOWED_client_server_request_response=334000
+      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=403000
 
   shell:
     image: swift-nio-http2:18.04-5.3
diff --git a/scripts/integration_tests.sh b/scripts/integration_tests.sh
index 083c59bf..ca630bd7 100755
--- a/scripts/integration_tests.sh
+++ b/scripts/integration_tests.sh
@@ -13,5 +13,7 @@
 ##
 ##===----------------------------------------------------------------------===##
 
+set +ex
+
 mkdir -p .build # for the junit.xml file
-./IntegrationTests/run-tests.sh --junit-xml .build/junit-sh-tests.xml -i
+./IntegrationTests/run-tests.sh --junit-xml .build/junit-sh-tests.xml -i $@