diff --git a/engine/table/src/main/java/io/deephaven/engine/table/impl/select/analyzers/SelectColumnLayer.java b/engine/table/src/main/java/io/deephaven/engine/table/impl/select/analyzers/SelectColumnLayer.java
index a9a12b0942f..7a291ee5858 100644
--- a/engine/table/src/main/java/io/deephaven/engine/table/impl/select/analyzers/SelectColumnLayer.java
+++ b/engine/table/src/main/java/io/deephaven/engine/table/impl/select/analyzers/SelectColumnLayer.java
@@ -568,6 +568,6 @@ public LogOutput append(LogOutput logOutput) {
 
     @Override
     public boolean allowCrossColumnParallelization() {
-        return inner.allowCrossColumnParallelization();
+        return selectColumn.isStateless() && inner.allowCrossColumnParallelization();
     }
 }