diff --git a/tests/kafkatest/tests/streams/streams_broker_down_resilience_test.py b/tests/kafkatest/tests/streams/streams_broker_down_resilience_test.py
index eea7f56f01b3..92e01b87c75b 100644
--- a/tests/kafkatest/tests/streams/streams_broker_down_resilience_test.py
+++ b/tests/kafkatest/tests/streams/streams_broker_down_resilience_test.py
@@ -100,7 +100,7 @@ def test_streams_runs_with_broker_down_initially(self, metadata_quorum):
         processor_3 = StreamsBrokerDownResilienceService(self.test_context, self.kafka, configs)
         processor_3.start()
 
-        broker_unavailable_message = "Broker may not be available"
+        broker_unavailable_message = "Node may not be available"
 
         # verify streams instances unable to connect to broker, kept trying
         self.wait_for_verification(processor, broker_unavailable_message, processor.LOG_FILE, 10)
diff --git a/tests/kafkatest/tests/streams/streams_upgrade_test.py b/tests/kafkatest/tests/streams/streams_upgrade_test.py
index 9039d9d7473a..955ce0295012 100644
--- a/tests/kafkatest/tests/streams/streams_upgrade_test.py
+++ b/tests/kafkatest/tests/streams/streams_upgrade_test.py
@@ -40,11 +40,13 @@
 metadata_1_versions = [str(LATEST_0_10_0)]
 metadata_2_versions = [str(LATEST_0_10_1), str(LATEST_0_10_2), str(LATEST_0_11_0), str(LATEST_1_0), str(LATEST_1_1),
                        str(LATEST_2_4), str(LATEST_2_5), str(LATEST_2_6), str(LATEST_2_7), str(LATEST_2_8),
-                       str(LATEST_3_0)]
-# upgrading from version (2.4...3.0) is broken and only fixed later in 3.1
-# we cannot test two bounce rolling upgrade because we know it's broken
-# instead we add version 2.4...3.0 to the `metadata_2_versions` upgrade list
-fk_join_versions = [str(LATEST_3_1), str(LATEST_3_2), str(LATEST_3_3)]
+                       str(LATEST_3_0), str(LATEST_3_1), str(LATEST_3_2), str(LATEST_3_3)]
+# upgrading from version (2.4...3.3) is broken and only fixed later in 3.3.3 (unreleased) and 3.4.0
+# -> https://issues.apache.org/jira/browse/KAFKA-14646
+# thus, we cannot test two bounce rolling upgrade because we know it's broken
+# instead we add version 2.4...3.3 to the `metadata_2_versions` upgrade list
+#fk_join_versions = [str(LATEST_3_4)]
+
 
 """
 After each release one should first check that the released version has been uploaded to 
@@ -202,7 +204,7 @@ def test_upgrade_downgrade_brokers(self, from_version, to_version):
     @cluster(num_nodes=6)
     @matrix(from_version=metadata_1_versions, to_version=[str(DEV_VERSION)])
     @matrix(from_version=metadata_2_versions, to_version=[str(DEV_VERSION)])
-    @matrix(from_version=fk_join_versions, to_version=[str(DEV_VERSION)])
+    #@matrix(from_version=fk_join_versions, to_version=[str(DEV_VERSION)])
     def test_rolling_upgrade_with_2_bounces(self, from_version, to_version):
         """
         This test verifies that the cluster successfully upgrades despite changes in the metadata and FK
diff --git a/tests/kafkatest/version.py b/tests/kafkatest/version.py
index ed0210d34537..8cebd955d40f 100644
--- a/tests/kafkatest/version.py
+++ b/tests/kafkatest/version.py
@@ -107,8 +107,10 @@ def supports_topic_ids_when_using_zk(self):
         return self >= V_2_8_0
 
     def supports_fk_joins(self):
-        # while we support FK joins since 2.4, rolling upgrade is broken in older versions and only fixed in 3.1
-        return hasattr(self, "version") and self >= V_3_1_2
+        # while we support FK joins since 2.4, rolling upgrade is broken in older versions
+        # it's only fixed in 3.3.3 (unreleased) and 3.4.0
+        # -> https://issues.apache.org/jira/browse/KAFKA-14646
+        return hasattr(self, "version") and self >= V_3_4_0
 
 def get_version(node=None):
     """Return the version attached to the given node.