diff --git a/newsfragments/73.feature.rst b/newsfragments/73.feature.rst
new file mode 100644
index 0000000..9993cdf
--- /dev/null
+++ b/newsfragments/73.feature.rst
@@ -0,0 +1,3 @@
+pytest-trio now makes the Trio scheduler deterministic while running
+inside a Hypothesis test.  Hopefully you won't see any change, but if
+you had scheduler-dependent bugs Hypothesis will be more effective now.
diff --git a/pytest_trio/plugin.py b/pytest_trio/plugin.py
index b567cf9..6de8ba8 100644
--- a/pytest_trio/plugin.py
+++ b/pytest_trio/plugin.py
@@ -22,6 +22,17 @@
     # Ordered dict (and **kwargs) not available with Python<3.6
     ORDERED_DICTS = False
 
+try:
+    import hypothesis.strategies as st
+except ImportError:
+    pass
+else:
+    # On recent versions of Hypothesis, make the Trio scheduler deterministic
+    # even though it uses a module-scoped Random instance.  This works
+    # regardless of whether or not the random_module strategy is used.
+    if hasattr(st.random_module, 'register'):
+        st.random_module.register(trio._core._run._r)
+
 
 def pytest_addoption(parser):
     parser.addini(