diff --git a/nbclient/tests/test_util.py b/nbclient/tests/test_util.py
index dc206826..1decb67e 100644
--- a/nbclient/tests/test_util.py
+++ b/nbclient/tests/test_util.py
@@ -1,10 +1,12 @@
 import asyncio
+import unittest.mock
 from unittest.mock import MagicMock
 
+import psutil  # type: ignore
 import pytest
 import tornado
 
-from nbclient.util import run_hook, run_sync
+from nbclient.util import just_run, run_hook, run_sync
 
 
 @run_sync
@@ -75,3 +77,27 @@ async def test_run_hook_async():
     hook = MagicMock(return_value=some_async_function())
     await run_hook(hook)
     assert hook.call_count == 1
+
+
+def test_just_run_doesnt_leak_fds():
+    proc = psutil.Process()
+
+    # Warmup, just to make sure we're not failing on some initial fds being opened for the first time.
+    for _ in range(10):
+        just_run(asyncio.sleep(0.01))
+    fds_count = proc.num_fds()
+
+    diff = []
+    for _ in range(10):
+        just_run(asyncio.sleep(0.01))
+        diff.append(proc.num_fds() - fds_count)
+    assert diff == [0] * 10
+
+
+def test_just_run_clears_new_loop():
+    loop = asyncio.new_event_loop()
+
+    with unittest.mock.patch.object(asyncio, "new_event_loop", return_value=loop):
+        just_run(asyncio.sleep(0.01))
+
+    assert loop.is_closed()
diff --git a/nbclient/util.py b/nbclient/util.py
index 0a352c2d..0b5af739 100644
--- a/nbclient/util.py
+++ b/nbclient/util.py
@@ -57,7 +57,11 @@ def just_run(coro: Awaitable) -> Any:
 
         nest_asyncio.apply()
         check_patch_tornado()
-    return loop.run_until_complete(coro)
+    res = loop.run_until_complete(coro)
+    if not had_running_loop:
+        loop.stop()
+        loop.close()
+    return res
 
 
 T = TypeVar("T")
diff --git a/requirements-dev.txt b/requirements-dev.txt
index ec1b95ec..37b26b36 100644
--- a/requirements-dev.txt
+++ b/requirements-dev.txt
@@ -7,6 +7,7 @@ ipywidgets<8.0.0
 mypy
 pip>=18.1
 pre-commit
+psutil
 pytest>=4.1
 pytest-asyncio
 pytest-cov>=2.6.1