diff --git a/tests/e2e/test_e2e.py b/tests/e2e/test_e2e.py
index 0aef1e738..410be28bd 100644
--- a/tests/e2e/test_e2e.py
+++ b/tests/e2e/test_e2e.py
@@ -503,3 +503,54 @@ class TestE2E(StepsFilter, StepsStore, StepsRelay, StepsLightPush):
             pubsub_topic=self.test_pubsub_topic, content_topics=self.test_content_topic, page_size=5, ascending="true"
         )
         assert len(store_response["messages"]) == 1, "Can't find stored message!!"
+
+    @pytest.mark.timeout(60 * 4)
+    def test_relay_2_nodes_bandwidth_high_vs_low(self):
+        self.node1 = WakuNode(NODE_1, f"node1_{self.test_id}")
+        self.node2 = WakuNode(NODE_2, f"node2_{self.test_id}")
+
+        self.node1.start(relay="true")
+        self.node2.start(relay="true", discv5_bootstrap_node=self.node1.get_enr_uri())
+
+        self.node1.set_relay_subscriptions([self.test_pubsub_topic])
+        self.node2.set_relay_subscriptions([self.test_pubsub_topic])
+
+        self.wait_for_autoconnection([self.node1, self.node2], hard_wait=10)
+
+        msg_count = 120
+        window_s = 20
+
+        self.tc.add_bandwidth(self.node2, rate="10mbit")
+
+        for _ in range(msg_count):
+            self.node1.send_relay_message(
+                self.create_message(),
+                self.test_pubsub_topic,
+            )
+
+        deadline = time() + window_s
+        high_bw_msgs = 0
+        while time() < deadline:
+            msgs = self.node2.get_relay_messages(self.test_pubsub_topic) or []
+            high_bw_msgs = max(high_bw_msgs, len(msgs))
+            sleep(0.5)
+
+        self.tc.add_bandwidth(self.node2, rate="256kbit")
+
+        for _ in range(msg_count):
+            self.node1.send_relay_message(
+                self.create_message(),
+                self.test_pubsub_topic,
+            )
+
+        deadline = time() + window_s
+        low_bw_msgs = 0
+        while time() < deadline:
+            msgs = self.node2.get_relay_messages(self.test_pubsub_topic) or []
+            low_bw_msgs = max(low_bw_msgs, len(msgs))
+            sleep(0.5)
+
+        logger.info(f"high_bw_msgs={high_bw_msgs} low_bw_msgs={low_bw_msgs} " f"msg_count={msg_count} window={window_s}s")
+
+        assert high_bw_msgs > 0
+        assert high_bw_msgs >= low_bw_msgs