diff --git a/datalad_next/runners/run.py b/datalad_next/runners/run.py
index 1f5593554..eef6731dc 100644
--- a/datalad_next/runners/run.py
+++ b/datalad_next/runners/run.py
@@ -6,6 +6,7 @@
 
 import logging
 import subprocess
+import sys
 from collections.abc import Generator
 from contextlib import contextmanager
 from pathlib import Path
@@ -257,14 +258,14 @@ def run(
         try:
             yield KillingResultGenerator(result)
         except:
-            import sys, time
             e = sys.exc_info()[1]
-            lgr.warning(
-                f'Possible stall: exception ({e!r}) raised in '
-                f'run-context ({cmd!r}), waiting for subprocess exit. If the '
-                f'subprocess exit was not triggered yet, and if no termination-'
-                f' or kill-timeout is active, this might wait forever.'
-            )
+            if kill_time is None:
+                lgr.warning(
+                    f'Possible stall: exception ({e!r}) raised in '
+                    f'run-context ({cmd!r}) without kill-timeout. Waiting for '
+                    f'subprocess exit, If subprocess exit was not triggered yet, '
+                    f'this might wait forever.'
+                )
             raise
         finally:
             # Arm the protocol, that will enable terminate signaling or kill
@@ -276,5 +277,9 @@ def run(
             # the result code of the terminated process.
             # NOTE: if terminate_time and kill_time are both None, this might
             # loop forever.
+            lgr.debug(
+                f'Waiting for termination of {cmd!r}, terminate_time: '
+                f'{terminate_time!r}, kill_time: {kill_time!r}'
+            )
             for _ in result:
                 pass
diff --git a/datalad_next/runners/tests/test_run.py b/datalad_next/runners/tests/test_run.py
index 8f35dc918..efa146293 100644
--- a/datalad_next/runners/tests/test_run.py
+++ b/datalad_next/runners/tests/test_run.py
@@ -8,7 +8,6 @@
 from pathlib import Path
 from queue import Queue
 from random import randint
-from typing import Generator
 
 import pytest
 
@@ -380,20 +379,32 @@ def test_run_nongenerator():
         assert res['stderr'] == 'error'
 
 
-def test_run_exception_in_context(monkeypatch):
-    # Check that an exception in the context is logged and re-raises:
+@pytest.mark.parametrize(
+    'termination_time,kill_time,expect_warning',
+    [
+        (1, None, True),
+        (None, 1, False),
+        (1, 1, False),
+        (None, None, True),
+    ]
+)
+def test_run_exception_in_context(monkeypatch, termination_time, kill_time, expect_warning):
+    # Check that an exception in the context is re-raised, and that a
+    # stall-warning is emitted, if no timeout was set.
     warnings = []
     monkeypatch.setattr(
         'datalad_next.runners.run.lgr.warning',
         lambda s: warnings.append(s)
     )
+
     with pytest.raises(ValueError):
-        with run([
-                sys.executable, '-u', '-c',
-                'import time\n'
-                'time.sleep(5)\n'
-            ],
-            StdOutCaptureGeneratorProtocol,
-        ):
+        with run([sys.executable, '-u', '-c', 'import time\ntime.sleep(2)\n'],
+                 StdOutCaptureGeneratorProtocol,
+                 terminate_time=termination_time,
+                 kill_time=kill_time):
             raise ValueError('Something')
-    assert warnings[0].startswith('Possible stall:')
+    if expect_warning:
+        assert len(warnings) == 1
+        assert warnings[0].startswith('Possible stall:')
+    else:
+        assert len(warnings) == 0