diff --git a/trio/_core/tests/test_run.py b/trio/_core/tests/test_run.py
index 5f4f232b1f..fc949290bd 100644
--- a/trio/_core/tests/test_run.py
+++ b/trio/_core/tests/test_run.py
@@ -11,7 +11,7 @@
 import pytest
 import attr
 
-from .tutil import check_sequence_matches
+from .tutil import check_sequence_matches, gc_collect_harder
 from ...testing import (
     wait_all_tasks_blocked, Sequencer, assert_yields,
 )
@@ -41,7 +41,8 @@ def ignore_coroutine_never_awaited_warnings():
         finally:
             # Make sure to trigger any coroutine __del__ methods now, before
             # we leave the context manager.
-            gc.collect()
+            gc_collect_harder()
+
 
 def test_basic():
     async def trivial(x):
@@ -883,7 +884,7 @@ async def main():
     # Because this crashes, various __del__ methods print complaints on
     # stderr. Make sure that they get run now, so the output is attached to
     # this test.
-    gc.collect()
+    gc_collect_harder()
 
 
 def test_error_in_run_loop():
@@ -1490,6 +1491,8 @@ async def f():  # pragma: no cover
                 bad_call(len, [1, 2, 3])
             assert "appears to be synchronous" in str(excinfo.value)
 
+            # Make sure no references are kept around to keep anything alive
+            del excinfo
 
 def test_calling_asyncio_function_gives_nice_error():
     async def misguided():
diff --git a/trio/_core/tests/tutil.py b/trio/_core/tests/tutil.py
index 0a38f21f24..c2e59157fa 100644
--- a/trio/_core/tests/tutil.py
+++ b/trio/_core/tests/tutil.py
@@ -2,13 +2,26 @@
 
 import pytest
 
+import gc
+
 # See trio/tests/conftest.py for the other half of this
 slow = pytest.mark.skipif(
     not pytest.config.getoption("--run-slow", True),
     reason="use --run-slow to run slow tests",
 )
 
-from ... import _core
+def gc_collect_harder():
+    # In the test suite we sometimes want to call gc.collect() to make sure
+    # that any objects with noisy __del__ methods (e.g. unawaited coroutines)
+    # get collected before we continue, so their noise doesn't leak into
+    # unrelated tests.
+    #
+    # On PyPy, coroutine objects (for example) can survive at least 1 round of
+    # garbage collection, because executing their __del__ method to print the
+    # warning can cause them to be resurrected. So we call collect a few times
+    # to make sure.
+    for _ in range(4):
+        gc.collect()
 
 # template is like:
 #   [1, {2.1, 2.2}, 3] -> matches [1, 2.1, 3] or [1, 2.2, 3]