diff --git a/hypothesis-python/src/hypothesis/internal/compat.py b/hypothesis-python/src/hypothesis/internal/compat.py
index dabc4b99c9..59cee0fbf4 100644
--- a/hypothesis-python/src/hypothesis/internal/compat.py
+++ b/hypothesis-python/src/hypothesis/internal/compat.py
@@ -27,6 +27,7 @@
 import codecs
 import platform
 import importlib
+import collections
 from base64 import b64encode
 from collections import namedtuple
 
@@ -35,6 +36,7 @@
 except ImportError:
     from ordereddict import OrderedDict  # type: ignore
     from counter import Counter  # type: ignore
+    from collections import Container
 
 if False:
     from typing import Type  # noqa
@@ -70,6 +72,7 @@ def int_to_text(i):
     ARG_NAME_ATTRIBUTE = 'arg'
     integer_types = (int,)
     hunichr = chr
+    Container = collections.abc.Container  # type: ignore
 
     def unicode_safe_repr(x):
         return repr(x)
@@ -217,6 +220,7 @@ def shimrange():
     ARG_NAME_ATTRIBUTE = 'id'
     integer_types = (int, long)
     hunichr = unichr
+    Container = collections.Container
 
     def escape_unicode_characters(s):
         return codecs.encode(s, 'string_escape')
diff --git a/hypothesis-python/src/hypothesis/searchstrategy/attrs.py b/hypothesis-python/src/hypothesis/searchstrategy/attrs.py
index 5c8f5ff50d..fd341f8974 100644
--- a/hypothesis-python/src/hypothesis/searchstrategy/attrs.py
+++ b/hypothesis-python/src/hypothesis/searchstrategy/attrs.py
@@ -26,6 +26,7 @@
 from hypothesis.errors import ResolutionFailed
 from hypothesis.internal.compat import string_types, get_type_hints
 from hypothesis.utils.conventions import infer
+from hypothesis.searchstrategy.types import type_sorting_key
 
 
 def from_attrs(target, args, kwargs, to_infer):
@@ -107,17 +108,21 @@ def types_to_strategy(attrib, types):
             return st.one_of(*map(st.from_type, typ))
         return st.from_type(typ)
     elif types:
-        # Multiple type validators.  Pick common type(s) that satisfy all.
-        # TODO: use a more sophisticated aggregation that understands subtypes,
-        # generic types, etc.  Consider pulling some code out of st.from_type?
+        # We have a list of tuples of types, and want to find a type
+        # (or tuple of types) that is a subclass of all of of them.
         type_tuples = [k if isinstance(k, tuple) else (k,) for k in types]
-        return st.one_of(*map(st.from_type, ordered_intersection(type_tuples)))
+        # Flatten the list, filter types that would fail validation, and
+        # sort so that ordering is stable between runs and shrinks well.
+        allowed = [t for t in set(sum(type_tuples, ()))
+                   if all(issubclass(t, tup) for tup in type_tuples)]
+        allowed.sort(key=type_sorting_key)
+        return st.one_of([st.from_type(t) for t in allowed])
 
     # Otherwise, try the `type` attribute as a fallback, and finally try
     # the type hints on a converter (desperate!) before giving up.
     if isinstance(getattr(attrib, 'type', None), type):
         # The convoluted test is because variable annotations may be stored
-        # in string form, and pass through attrs unevaluated.
+        # in string form; attrs doesn't evaluate them and we don't handle them.
         # See PEP 526, PEP 563, and Hypothesis issue #1004 for details.
         return st.from_type(attrib.type)
 
diff --git a/hypothesis-python/src/hypothesis/searchstrategy/types.py b/hypothesis-python/src/hypothesis/searchstrategy/types.py
index 86cfa581b3..a39a2c01e3 100644
--- a/hypothesis-python/src/hypothesis/searchstrategy/types.py
+++ b/hypothesis-python/src/hypothesis/searchstrategy/types.py
@@ -27,7 +27,7 @@
 
 import hypothesis.strategies as st
 from hypothesis.errors import InvalidArgument, ResolutionFailed
-from hypothesis.internal.compat import PY2, text_type
+from hypothesis.internal.compat import PY2, Container, text_type
 
 
 def type_sorting_key(t):
@@ -35,8 +35,8 @@ def type_sorting_key(t):
     if not isinstance(t, type):
         raise InvalidArgument('thing=%s must be a type' % (t,))
     if t is None or t is type(None):  # noqa: E721
-        return -1
-    return issubclass(t, collections.abc.Container)
+        return (-1, repr(t))
+    return (issubclass(t, Container), repr(t))
 
 
 def try_issubclass(thing, maybe_superclass):
diff --git a/hypothesis-python/tests/cover/test_attrs_inference.py b/hypothesis-python/tests/cover/test_attrs_inference.py
index 0b6e3fdc79..b9e18c729f 100644
--- a/hypothesis-python/tests/cover/test_attrs_inference.py
+++ b/hypothesis-python/tests/cover/test_attrs_inference.py
@@ -37,6 +37,11 @@ class Inferrables(object):
         attr.validators.instance_of(str),
         attr.validators.instance_of((str, int, bool)),
     ])
+    validator_type_has_overlap = attr.ib(validator=[
+        attr.validators.instance_of(str),
+        attr.validators.instance_of((str, list)),
+        attr.validators.instance_of(object),
+    ])
     validator_optional = attr.ib(
         validator=attr.validators.optional(lambda inst, atrib, val: float(val))
     )