diff --git a/ci/builder/requirements.txt b/ci/builder/requirements.txt
index c85a860cb0435..23f3d61501f6c 100644
--- a/ci/builder/requirements.txt
+++ b/ci/builder/requirements.txt
@@ -50,9 +50,8 @@ pdoc==16.0.0
 pg8000==1.31.6
 prettytable==3.18.0
 psutil==7.2.2
-# TODO: Bump psycopg/psycopg-binary to >= 3.3.6 when SQL-840 is fixed
-psycopg==3.3.3
-psycopg-binary==3.3.3
+psycopg==3.3.6
+psycopg-binary==3.3.6
 pydantic==2.14.1
 pyelftools==0.33
 pyjwt==2.15.1
diff --git a/src/pgwire/src/protocol.rs b/src/pgwire/src/protocol.rs
index 103267937ccdc..04e2f1965ae2a 100644
--- a/src/pgwire/src/protocol.rs
+++ b/src/pgwire/src/protocol.rs
@@ -1485,12 +1485,14 @@ where
                 self.send_parameter_statuses(params).await?;
             }
             Ok(_) => {}
-            Err(err) => {
+            Err(err) if action == EndTransactionAction::Commit => {
                 self.send(BackendMessage::ErrorResponse(
                     err.into_response(Severity::Error),
                 ))
                 .await?;
             }
+            // Only one error can be reported, ignore.
+            Err(_) => {}
         }
         Ok(())
     }
diff --git a/test/cluster/mzcompose.py b/test/cluster/mzcompose.py
index 3c7ba8f4038ef..498c903f842e8 100644
--- a/test/cluster/mzcompose.py
+++ b/test/cluster/mzcompose.py
@@ -3302,6 +3302,25 @@ def fetch_metrics() -> Metrics:
     assert 0 < time < 10, f"got {time}"
 
 
+def workflow_test_dropped_role_begin(c: Composition) -> None:
+    c.up("materialized")
+    c.sql("CREATE ROLE dropped_role")
+
+    with c.sql_connection(user="dropped_role") as conn:
+        conn.autocommit = False
+        c.sql("DROP ROLE dropped_role")
+
+        # Psycopg first sends an implicit BEGIN. Duplicate error responses
+        # mask the dropped-role error with a client-side InternalError.
+        try:
+            conn.execute("SELECT 1")
+        except psycopg.errors.InsufficientPrivilege as e:
+            assert "was concurrently dropped" in str(e), str(e)
+            assert conn.info.transaction_status == psycopg.pq.TransactionStatus.IDLE
+        else:
+            raise AssertionError("query succeeded after its role was dropped")
+
+
 def workflow_test_pgwire_metrics(c: Composition) -> None:
     """Test metrics collected in the Adapter frontend, i.e., `pgwire.rs`"""