diff --git a/tests/utils/test_compute_node.py b/tests/utils/test_compute_node.py
index bb16b84d..c9259324 100644
--- a/tests/utils/test_compute_node.py
+++ b/tests/utils/test_compute_node.py
@@ -221,30 +221,44 @@ async def test_run_gets_executed_in_job_step(
         assert job_step_b == job_step_a + 1
 
     @pytest.mark.asyncio
-    async def test_connect(self, runner: ComputeNode):
+    async def test_connect_with_job_id(self, runner: ComputeNode):
         login_node = runner.login_node
         job_id = runner.job_id
-        node_hostname = runner.hostname
+        # Connect with the job id:
         compute_node_with_jobid = await ComputeNode.connect(
             login_node, job_id_or_node_name=job_id
         )
         assert compute_node_with_jobid.salloc_subprocess is None
+        # Note: __eq__ from dataclass ignores some fields in this case (those with
+        # compare=False), in this case the salloc_subprocess is different, but the
+        # equality check succeeds
         assert compute_node_with_jobid == runner
 
+    @pytest.mark.asyncio
+    async def test_connect_with_node_name(self, runner: ComputeNode):
+        """Test connecting to a compute node using the node name.
+
+        This will probably eventually be deprecated in favour of reconnecting with the
+        job ID instead, since it's unambiguous in the case of multiple jobs running on
+        the same node.
+        """
         # Need to connect with the node name, not the full node hostname.
         # For the `mila` cluster, we don't currently have a `cn-?????` entry in the ssh
         # config (although we could!)
         # Therefore, we need to connect to the node with the full hostname. However
         # squeue expects the node name, so we have to truncate it manually for now.
+        login_node = runner.login_node
+        node_hostname = runner.hostname
         if node_hostname.endswith(".server.mila.quebec"):
             node_name = removesuffix(node_hostname, ".server.mila.quebec")
         else:
             node_name = node_hostname
 
+        # Connect with the node name:
         compute_node_with_node_name = await ComputeNode.connect(
             login_node, job_id_or_node_name=node_name
         )
-        assert compute_node_with_jobid.salloc_subprocess is None
+        assert compute_node_with_node_name.salloc_subprocess is None
         assert compute_node_with_node_name == runner
 
     @pytest.mark.parametrize("use_async", [False, True], ids=["sync", "async"])