diff --git a/hypothesis-python/RELEASE.rst b/hypothesis-python/RELEASE.rst
new file mode 100644
index 0000000000..80da08b2dc
--- /dev/null
+++ b/hypothesis-python/RELEASE.rst
@@ -0,0 +1,6 @@
+RELEASE_TYPE: patch
+
+This patch improves the performance of unique collections such as
+:func:`~hypothesis.strategies.sets` of :func:`~hypothesis.strategies.just`
+or :func:`~hypothesis.strategies.booleans` strategies.  They were already
+pretty good though, so you're unlikely to notice much!
diff --git a/hypothesis-python/src/hypothesis/_strategies.py b/hypothesis-python/src/hypothesis/_strategies.py
index 48b0ab5d1e..8ad0412f57 100644
--- a/hypothesis-python/src/hypothesis/_strategies.py
+++ b/hypothesis-python/src/hypothesis/_strategies.py
@@ -96,11 +96,7 @@
 from hypothesis.searchstrategy.deferred import DeferredStrategy
 from hypothesis.searchstrategy.functions import FunctionStrategy
 from hypothesis.searchstrategy.lazy import LazyStrategy
-from hypothesis.searchstrategy.misc import (
-    BoolStrategy,
-    JustStrategy,
-    SampledFromStrategy,
-)
+from hypothesis.searchstrategy.misc import JustStrategy, SampledFromStrategy
 from hypothesis.searchstrategy.numbers import (
     BoundedIntStrategy,
     FixedBoundedFloatStrategy,
@@ -425,7 +421,7 @@ def booleans():
     Examples from this strategy will shrink towards False (i.e.
     shrinking will try to replace True with False where possible).
     """
-    return BoolStrategy()
+    return sampled_from([False, True])
 
 
 @cacheable
diff --git a/hypothesis-python/src/hypothesis/searchstrategy/misc.py b/hypothesis-python/src/hypothesis/searchstrategy/misc.py
index 668acdbd8b..8f27740a1f 100644
--- a/hypothesis-python/src/hypothesis/searchstrategy/misc.py
+++ b/hypothesis-python/src/hypothesis/searchstrategy/misc.py
@@ -22,20 +22,6 @@
 from hypothesis.searchstrategy.strategies import SearchStrategy, filter_not_satisfied
 
 
-class BoolStrategy(SearchStrategy):
-    """A strategy that produces Booleans with a Bernoulli conditional
-    distribution."""
-
-    def __repr__(self):
-        return "BoolStrategy()"
-
-    def calc_has_reusable_values(self, recur):
-        return True
-
-    def do_draw(self, data):
-        return d.boolean(data)
-
-
 def is_simple_data(value):
     try:
         hash(value)
@@ -44,26 +30,6 @@ def is_simple_data(value):
         return False
 
 
-class JustStrategy(SearchStrategy):
-    """A strategy which always returns a single fixed value."""
-
-    def __init__(self, value):
-        SearchStrategy.__init__(self)
-        self.value = value
-
-    def __repr__(self):
-        return "just(%r)" % (self.value,)
-
-    def calc_has_reusable_values(self, recur):
-        return True
-
-    def calc_is_cacheable(self, recur):
-        return is_simple_data(self.value)
-
-    def do_draw(self, data):
-        return self.value
-
-
 class SampledFromStrategy(SearchStrategy):
     """A strategy which samples from a set of elements. This is essentially
     equivalent to using a OneOfStrategy over Just strategies but may be more
@@ -154,3 +120,30 @@ def check_index(i):
         # If there are no allowed indices, the filter couldn't be satisfied.
 
         return filter_not_satisfied
+
+
+class JustStrategy(SampledFromStrategy):
+    """A strategy which always returns a single fixed value.
+
+    It's implemented as a length-one SampledFromStrategy so that all our
+    special-case logic for filtering and sets applies also to just(x).
+    """
+
+    def __init__(self, value):
+        SampledFromStrategy.__init__(self, [value])
+
+    @property
+    def value(self):
+        return self.elements[0]
+
+    def __repr__(self):
+        return "just(%r)" % (self.value,)
+
+    def calc_has_reusable_values(self, recur):
+        return True
+
+    def calc_is_cacheable(self, recur):
+        return is_simple_data(self.value)
+
+    def do_draw(self, data):
+        return self.value
diff --git a/hypothesis-python/src/hypothesis/stateful.py b/hypothesis-python/src/hypothesis/stateful.py
index 91f9c3b224..aceb9b7f65 100644
--- a/hypothesis-python/src/hypothesis/stateful.py
+++ b/hypothesis-python/src/hypothesis/stateful.py
@@ -42,7 +42,7 @@
 )
 from hypothesis.control import current_build_context
 from hypothesis.core import given
-from hypothesis.errors import HypothesisException, InvalidArgument, InvalidDefinition
+from hypothesis.errors import InvalidArgument, InvalidDefinition
 from hypothesis.internal.compat import quiet_raise, string_types
 from hypothesis.internal.reflection import function_digest, nicerepr, proxies
 from hypothesis.internal.validation import check_type
@@ -606,12 +606,10 @@ def __init__(self, machine):
         )
 
     def do_draw(self, data):
-        try:
-            rule = data.draw(st.sampled_from(self.rules).filter(self.is_valid))
-        except HypothesisException:
-            # FailedHealthCheck or UnsatisfiedAssumption depending on user settings.
+        if not any(self.is_valid(rule) for rule in self.rules):
             msg = u"No progress can be made from state %r" % (self.machine,)
             quiet_raise(InvalidDefinition(msg))
+        rule = data.draw(st.sampled_from(self.rules).filter(self.is_valid))
         return (rule, data.draw(rule.arguments_strategy))
 
     def is_valid(self, rule):
diff --git a/hypothesis-python/tests/cover/test_simple_collections.py b/hypothesis-python/tests/cover/test_simple_collections.py
index 7bc8f2192c..0bd7a4bdf0 100644
--- a/hypothesis-python/tests/cover/test_simple_collections.py
+++ b/hypothesis-python/tests/cover/test_simple_collections.py
@@ -155,10 +155,7 @@ def test_can_draw_empty_set_from_unsatisfiable_strategy():
     assert find_any(sets(integers().filter(lambda s: False))) == set()
 
 
-small_set = sets(none())
-
-
-@given(lists(small_set, min_size=10))
+@given(lists(sets(none()), min_size=10))
 def test_small_sized_sets(x):
     pass