diff --git a/hypothesis-python/RELEASE.rst b/hypothesis-python/RELEASE.rst
new file mode 100644
index 0000000000..7b28e79746
--- /dev/null
+++ b/hypothesis-python/RELEASE.rst
@@ -0,0 +1,6 @@
+RELEASE_TYPE: patch
+
+This patch changes the backing datastructures of :func:`~hypothesis.register_random`
+and a few internal caches to use :class:`weakref.WeakKeyDictionary`.  This reduces
+memory usage and may improve performance when registered :class:`~random.Random`
+instances are only used for a subset of your tests (:issue:`3131`).
diff --git a/hypothesis-python/src/hypothesis/internal/entropy.py b/hypothesis-python/src/hypothesis/internal/entropy.py
index 78b425720a..39c53ef578 100644
--- a/hypothesis-python/src/hypothesis/internal/entropy.py
+++ b/hypothesis-python/src/hypothesis/internal/entropy.py
@@ -16,10 +16,16 @@
 import contextlib
 import random
 import sys
+from itertools import count
+from weakref import WeakValueDictionary
 
 from hypothesis.errors import InvalidArgument
 
-RANDOMS_TO_MANAGE: list = [random]
+# This is effectively a WeakSet, which allows us to associate the saved states
+# with their respective Random instances even as new ones are registered and old
+# ones go out of scope and get garbage collected.  Keys are ascending integers.
+_RKEY = count()
+RANDOMS_TO_MANAGE: WeakValueDictionary = WeakValueDictionary({next(_RKEY): random})
 
 
 class NumpyRandomWrapper:
@@ -34,6 +40,9 @@ def __init__(self):
         self.setstate = numpy.random.set_state
 
 
+NP_RANDOM = None
+
+
 def register_random(r: random.Random) -> None:
     """Register the given Random instance for management by Hypothesis.
 
@@ -49,8 +58,8 @@ def register_random(r: random.Random) -> None:
     """
     if not (hasattr(r, "seed") and hasattr(r, "getstate") and hasattr(r, "setstate")):
         raise InvalidArgument(f"r={r!r} does not have all the required methods")
-    if r not in RANDOMS_TO_MANAGE:
-        RANDOMS_TO_MANAGE.append(r)
+    if r not in RANDOMS_TO_MANAGE.values():
+        RANDOMS_TO_MANAGE[next(_RKEY)] = r
 
 
 def get_seeder_and_restorer(seed=0):
@@ -64,24 +73,26 @@ def get_seeder_and_restorer(seed=0):
     using the global random state.  See e.g. #1709.
     """
     assert isinstance(seed, int) and 0 <= seed < 2 ** 32
-    states: list = []
+    states: dict = {}
 
-    if "numpy" in sys.modules and not any(
-        isinstance(x, NumpyRandomWrapper) for x in RANDOMS_TO_MANAGE
-    ):
-        RANDOMS_TO_MANAGE.append(NumpyRandomWrapper())
+    if "numpy" in sys.modules:
+        global NP_RANDOM
+        if NP_RANDOM is None:
+            # Protect this from garbage-collection by adding it to global scope
+            NP_RANDOM = RANDOMS_TO_MANAGE[next(_RKEY)] = NumpyRandomWrapper()
 
     def seed_all():
         assert not states
-        for r in RANDOMS_TO_MANAGE:
-            states.append(r.getstate())
+        for k, r in RANDOMS_TO_MANAGE.items():
+            states[k] = r.getstate()
             r.seed(seed)
 
     def restore_all():
-        assert len(states) == len(RANDOMS_TO_MANAGE)
-        for r, state in zip(RANDOMS_TO_MANAGE, states):
-            r.setstate(state)
-        del states[:]
+        for k, state in states.items():
+            r = RANDOMS_TO_MANAGE.get(k)
+            if r is not None:  # i.e., hasn't been garbage-collected
+                r.setstate(state)
+        states.clear()
 
     return seed_all, restore_all
 
diff --git a/hypothesis-python/src/hypothesis/strategies/_internal/lazy.py b/hypothesis-python/src/hypothesis/strategies/_internal/lazy.py
index aff1bce0df..92847a1cfe 100644
--- a/hypothesis-python/src/hypothesis/strategies/_internal/lazy.py
+++ b/hypothesis-python/src/hypothesis/strategies/_internal/lazy.py
@@ -14,7 +14,8 @@
 # END HEADER
 
 from inspect import getfullargspec
-from typing import Dict
+from typing import MutableMapping
+from weakref import WeakKeyDictionary
 
 from hypothesis.internal.reflection import (
     arg_string,
@@ -24,7 +25,7 @@
 )
 from hypothesis.strategies._internal.strategies import SearchStrategy
 
-unwrap_cache: Dict[SearchStrategy, SearchStrategy] = {}
+unwrap_cache: MutableMapping[SearchStrategy, SearchStrategy] = WeakKeyDictionary()
 unwrap_depth = 0
 
 
diff --git a/hypothesis-python/tests/cover/test_random_module.py b/hypothesis-python/tests/cover/test_random_module.py
index 14d7d25b61..4bccd93ca2 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 core, 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):
@@ -54,11 +65,15 @@ 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 entropy.RANDOMS_TO_MANAGE.pop() is r
-    assert r not in entropy.RANDOMS_TO_MANAGE
+    assert len(entropy.RANDOMS_TO_MANAGE) == n_registered + 1
+    del r
+    gc_on_pypy()
+    assert len(entropy.RANDOMS_TO_MANAGE) == n_registered
 
 
 def test_manages_registered_Random_instance():
@@ -78,9 +93,6 @@ def inner(x):
     inner()
     assert state == r.getstate()
 
-    entropy.RANDOMS_TO_MANAGE.remove(r)
-    assert r not in entropy.RANDOMS_TO_MANAGE
-
 
 def test_registered_Random_is_seeded_by_random_module_strategy():
     r = random.Random()
@@ -98,9 +110,6 @@ def inner(x):
     assert count[0] > len(results) * 0.9, "too few unique random numbers"
     assert state == r.getstate()
 
-    entropy.RANDOMS_TO_MANAGE.remove(r)
-    assert r not in entropy.RANDOMS_TO_MANAGE
-
 
 @given(st.random_module())
 def test_will_actually_use_the_random_seed(rnd):
@@ -143,3 +152,33 @@ def test_find_does_not_pollute_state():
 
         assert state_a == state_b
         assert state_a2 != state_b2
+
+
+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()
+
+    # We're going to be totally evil here: register two randoms, then
+    # drop one and add another, and finally check that we reset only
+    # the states that we collected before we started
+    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
+        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 r2.getstate() == s2, "reset previously registered random state"
+    assert r3.getstate() == s4, "retained state when registered within the context"