diff --git a/tests/system/test_observability_options.py b/tests/system/test_observability_options.py
index 9a006462be..ad535c57cb 100644
--- a/tests/system/test_observability_options.py
+++ b/tests/system/test_observability_options.py
@@ -100,7 +100,8 @@ def test_propagation(enable_extended_tracing):
                 _ = val
 
         from_global_spans = global_trace_exporter.get_finished_spans()
-        from_inject_spans = inject_trace_exporter.get_finished_spans()
+        target_spans = inject_trace_exporter.get_finished_spans()
+        from_inject_spans = sorted(target_spans, key=lambda v1: v1.start_time)
         assert (
             len(from_global_spans) == 0
         )  # "Expecting no spans from the global trace exporter"
@@ -111,7 +112,6 @@ def test_propagation(enable_extended_tracing):
         wantNames = [
             "CloudSpanner.CreateSession",
             "CloudSpanner.Snapshot.execute_streaming_sql",
-            "CloudSpanner.Database.snapshot",
         ]
         assert gotNames == wantNames
 
diff --git a/tests/system/test_session_api.py b/tests/system/test_session_api.py
index bcc2b552a8..d2a86c8ddf 100644
--- a/tests/system/test_session_api.py
+++ b/tests/system/test_session_api.py
@@ -463,24 +463,7 @@ def test_batch_insert_then_read(sessions_database, ot_exporter):
             span=span_list[3],
         )
 
-        assert_span_attributes(
-            ot_exporter,
-            "CloudSpanner.GetSession",
-            attributes=_make_attributes(db_name, session_found=True),
-            span=span_list[4],
-        )
-        assert_span_attributes(
-            ot_exporter,
-            "CloudSpanner.Snapshot.read",
-            attributes=_make_attributes(db_name, columns=sd.COLUMNS, table_id=sd.TABLE),
-            span=span_list[5],
-        )
-        assert_span_attributes(
-            ot_exporter,
-            "CloudSpanner.Database.snapshot",
-            attributes=_make_attributes(db_name, multi_use=False),
-            span=span_list[6],
-        )
+        assert len(span_list) == 4
 
 
 def test_batch_insert_then_read_string_array_of_string(sessions_database, not_postgres):