diff --git a/hypothesis-python/tests/cover/test_random_module.py b/hypothesis-python/tests/cover/test_random_module.py
index 71f55b9191..aa8b36931a 100644
--- a/hypothesis-python/tests/cover/test_random_module.py
+++ b/hypothesis-python/tests/cover/test_random_module.py
@@ -13,6 +13,7 @@
 #
 # END HEADER
 
+import gc
 import random
 
 import pytest
@@ -20,11 +21,21 @@
 from hypothesis import find, given, register_random, reporting, strategies as st
 from hypothesis.errors import InvalidArgument
 from hypothesis.internal import entropy
+from hypothesis.internal.compat import PYPY
 from hypothesis.internal.entropy import deterministic_PRNG
 
 from tests.common.utils import capture_out
 
 
+def gc_on_pypy():
+    # CPython uses reference counting, so objects (without circular refs)
+    # are collected immediately on `del`, breaking weak references.
+    # PyPy doesn't, so we use this function in tests before counting the
+    # surviving references to ensure that they're deterministic.
+    if PYPY:
+        gc.collect()
+
+
 def test_can_seed_random():
     with capture_out() as out:
         with reporting.with_reporter(reporting.default):
@@ -54,12 +65,14 @@ def test_cannot_register_non_Random():
 
 
 def test_registering_a_Random_is_idempotent():
+    gc_on_pypy()
     n_registered = len(entropy.RANDOMS_TO_MANAGE)
     r = random.Random()
     register_random(r)
     register_random(r)
     assert len(entropy.RANDOMS_TO_MANAGE) == n_registered + 1
     del r
+    gc_on_pypy()
     assert len(entropy.RANDOMS_TO_MANAGE) == n_registered
 
 
@@ -136,6 +149,7 @@ def test_find_does_not_pollute_state():
 
 
 def test_evil_prng_registration_nonsense():
+    gc_on_pypy()
     n_registered = len(entropy.RANDOMS_TO_MANAGE)
     r1, r2, r3 = random.Random(1), random.Random(2), random.Random(3)
     s2 = r2.getstate()
@@ -146,16 +160,19 @@ def test_evil_prng_registration_nonsense():
     register_random(r1)
     k = max(entropy.RANDOMS_TO_MANAGE)  # get a handle to check if r1 still exists
     register_random(r2)
+    assert len(entropy.RANDOMS_TO_MANAGE) == n_registered + 2
+
     with deterministic_PRNG(0):
         del r1
-        r2.seed(4)
+        gc_on_pypy()
+        assert k not in entropy.RANDOMS_TO_MANAGE, "r1 has been garbage-collected"
         assert len(entropy.RANDOMS_TO_MANAGE) == n_registered + 1
 
+        r2.seed(4)
         register_random(r3)
         r3.seed(4)
         s4 = r3.getstate()
 
     # Implicit check, no exception was raised in __exit__
-    assert k not in entropy.RANDOMS_TO_MANAGE, "r1 has been garbage-collected"
     assert r2.getstate() == s2, "reset previously registered random state"
     assert r3.getstate() == s4, "retained state when registered within the context"