diff --git a/integration_tests/src/main/python/orc_test.py b/integration_tests/src/main/python/orc_test.py
index 789a261b52b..618004ee60d 100644
--- a/integration_tests/src/main/python/orc_test.py
+++ b/integration_tests/src/main/python/orc_test.py
@@ -845,12 +845,16 @@ def test_simple_partitioned_read_for_multithreaded_combining(spark_tmp_path, kee
     assert_gpu_and_cpu_are_equal_collect(
         lambda spark: spark.read.orc(data_path), conf=all_confs)
 
-@pytest.mark.skipif(is_spark_340_or_later() and (not (is_databricks_runtime() and spark_version() == "3.4.1")), reason="https://github.com/NVIDIA/spark-rapids/issues/8324")
+
+@pytest.mark.skipif(is_spark_340_or_later() and not is_databricks_runtime(),
+                    reason="https://github.com/NVIDIA/spark-rapids/issues/8324")
 @pytest.mark.parametrize('data_file', ['fixed-length-char-column-from-hive.orc'])
 @pytest.mark.parametrize('reader', [read_orc_df, read_orc_sql])
 def test_read_hive_fixed_length_char(std_input_path, data_file, reader):
     """
     Test that a file containing CHAR data is readable as STRING.
+    The plugin behaviour matches all Spark versions prior to 3.4.0,
+    and Databricks version 13.3 (i.e. 3.4.1) and after.
     """
     assert_gpu_and_cpu_are_equal_collect(
         reader(std_input_path + '/' + data_file),
@@ -858,20 +862,30 @@ def test_read_hive_fixed_length_char(std_input_path, data_file, reader):
 
 
 @allow_non_gpu("ProjectExec")
-@pytest.mark.skipif(is_before_spark_340() or (is_databricks_runtime() and spark_version() == "3.4.1"), reason="https://github.com/NVIDIA/spark-rapids/issues/8324")
+@pytest.mark.skipif(is_before_spark_340(),
+                    reason="https://github.com/NVIDIA/spark-rapids/issues/8324")
+@pytest.mark.skipif(is_databricks_version_or_later(13, 3),
+                    reason="The SELECT * query does not involve ProjectExec "
+                           "on Databricks versions >= 13.3. "
+                           "Can't test Project fallback without ProjectExec.")
 @pytest.mark.parametrize('data_file', ['fixed-length-char-column-from-hive.orc'])
 @pytest.mark.parametrize('reader', [read_orc_df, read_orc_sql])
 def test_project_fallback_when_reading_hive_fixed_length_char(std_input_path, data_file, reader):
     """
-    Test that a file containing CHAR data is readable as STRING.
+    Test that reading a file containing fixed-width CHAR data (e.g. CHAR(3)) as a STRING column
+    causes the ProjectExec to fall back to CPU.
     Note: This test can be removed when
     https://github.com/NVIDIA/spark-rapids/issues/8324 is resolved.
+
+    This test does not apply to Databricks >= 13.3, because there would be
+    no ProjectExec to fall back to CPU.
     """
     assert_gpu_fallback_collect(
         reader(std_input_path + '/' + data_file),
         cpu_fallback_class_name="ProjectExec",
         conf={})
 
+
 @pytest.mark.parametrize('read_func', [read_orc_df, read_orc_sql])
 @pytest.mark.parametrize('v1_enabled_list', ["", "orc"])
 @pytest.mark.parametrize('orc_impl', ["native", "hive"])