diff --git a/hypothesis-python/tests/cover/test_lookup.py b/hypothesis-python/tests/cover/test_lookup.py
index cc5e11c3f2..5653dc2c72 100644
--- a/hypothesis-python/tests/cover/test_lookup.py
+++ b/hypothesis-python/tests/cover/test_lookup.py
@@ -1149,6 +1149,7 @@ def test_resolves_builtin_types(t):
 
 @pytest.mark.parametrize("t", BUILTIN_TYPES, ids=lambda t: t.__name__)
 @given(data=st.data())
+@settings(max_examples=20)
 def test_resolves_forwardrefs_to_builtin_types(t, data):
     s = st.from_type(typing.ForwardRef(t.__name__))
     v = data.draw(s)
diff --git a/hypothesis-python/tests/nocover/test_characters.py b/hypothesis-python/tests/nocover/test_characters.py
index f736f784f9..b0a1c9913a 100644
--- a/hypothesis-python/tests/nocover/test_characters.py
+++ b/hypothesis-python/tests/nocover/test_characters.py
@@ -57,6 +57,7 @@ def _enc(cdc):
     reason="takes 2000s; large & slow symbolic strings",
 )
 @given(data=st.data(), codec=st.sampled_from(lots_of_encodings))
+@settings(max_examples=20)
 def test_can_constrain_characters_to_codec(data, codec):
-    s = data.draw(st.text(st.characters(codec=codec), min_size=100))
+    s = data.draw(st.text(st.characters(codec=codec), min_size=50))
     s.encode(codec)
diff --git a/hypothesis-python/tests/nocover/test_health_checks.py b/hypothesis-python/tests/nocover/test_health_checks.py
index e63ade92ca..abd9a78486 100644
--- a/hypothesis-python/tests/nocover/test_health_checks.py
+++ b/hypothesis-python/tests/nocover/test_health_checks.py
@@ -13,7 +13,7 @@
 import pytest
 from pytest import raises
 
-from hypothesis import HealthCheck, Phase, given, settings, strategies as st
+from hypothesis import HealthCheck, Phase, given, seed, settings, strategies as st
 from hypothesis.errors import FailedHealthCheck
 from hypothesis.internal.conjecture.data import ConjectureData
 from hypothesis.internal.conjecture.engine import BUFFER_SIZE
@@ -107,21 +107,22 @@ def test(n):
             test()
 
 
-def test_does_not_trigger_health_check_when_most_examples_are_small(monkeypatch):
-    with deterministic_PRNG():
-        for _ in range(100):
-            # Setting max_examples=11 ensures we have enough examples for the
-            # health checks to finish running, but cuts the generation short
-            # after that point to allow this test to run in reasonable time.
-            @settings(database=None, max_examples=11, phases=[Phase.generate])
-            @given(
-                st.integers(0, 100).flatmap(
-                    lambda n: st.binary(
-                        min_size=min(n * 100, BUFFER_SIZE), max_size=n * 100
-                    )
+def test_does_not_trigger_health_check_when_most_examples_are_small():
+    for i in range(10):
+
+        @seed(i)
+        # Setting max_examples=11 ensures we have enough examples for the
+        # health checks to finish running, but cuts the generation short
+        # after that point to allow this test to run in reasonable time.
+        @settings(database=None, max_examples=11, phases=[Phase.generate])
+        @given(
+            st.integers(0, 100).flatmap(
+                lambda n: st.binary(
+                    min_size=min(n * 100, BUFFER_SIZE), max_size=n * 100
                 )
             )
-            def test(b):
-                pass
+        )
+        def test(b):
+            pass
 
-            test()
+        test()
diff --git a/hypothesis-python/tests/watchdog/test_database.py b/hypothesis-python/tests/watchdog/test_database.py
index 1d1ec3ee5c..f3e253c830 100644
--- a/hypothesis-python/tests/watchdog/test_database.py
+++ b/hypothesis-python/tests/watchdog/test_database.py
@@ -45,7 +45,7 @@ def test_database_listener_directory():
 # seen flaky on test-win; we get *three* of the same save events in the first
 # assertion, which...is baffling, and possibly a genuine bug (most likely in
 # watchdog).
-@flaky(max_runs=2, min_passes=1)
+@flaky(max_runs=5, min_passes=1)
 def test_database_listener_multiplexed(tmp_path):
     db = MultiplexedDatabase(
         InMemoryExampleDatabase(), DirectoryBasedExampleDatabase(tmp_path)
@@ -96,7 +96,7 @@ def wait_for(condition, *, timeout=1, interval=0.01):
 
 
 # seen flaky on check-coverage (timeout in first wait_for)
-@flaky(max_runs=2, min_passes=1)
+@flaky(max_runs=5, min_passes=1)
 def test_database_listener_directory_explicit(tmp_path):
     db = DirectoryBasedExampleDatabase(tmp_path)
     events = []
@@ -167,7 +167,7 @@ def listener(event):
 
 
 # seen flaky on windows CI (timeout in wait_for)
-@flaky(max_runs=2, min_passes=1)
+@flaky(max_runs=5, min_passes=1)
 def test_database_listener_directory_move(tmp_path):
     db = DirectoryBasedExampleDatabase(tmp_path)
     events = []