diff --git a/openapi_core/schema/schemas/models.py b/openapi_core/schema/schemas/models.py
index fd26ce7..7353dd0 100644
--- a/openapi_core/schema/schemas/models.py
+++ b/openapi_core/schema/schemas/models.py
@@ -161,6 +161,13 @@ class Schema(object):
 
         return defaultdict(lambda: lambda x: x, mapping)
 
+    def are_additional_properties_allowed(self, one_of_schema=None):
+        return (
+            (self.additional_properties is not False) and
+            (one_of_schema is None or
+                one_of_schema.additional_properties is not False)
+        )
+
     def cast(self, value, custom_formatters=None, strict=True):
         """Cast value to schema type"""
         if value is None:
@@ -311,7 +318,9 @@ class Schema(object):
 
         value_props_names = value.keys()
         extra_props = set(value_props_names) - set(all_props_names)
-        if extra_props and self.additional_properties is False:
+        extra_props_allowed = self.are_additional_properties_allowed(
+            one_of_schema)
+        if extra_props and not extra_props_allowed:
             raise UndefinedSchemaProperty(extra_props)
 
         properties = {}
@@ -543,7 +552,9 @@ class Schema(object):
 
         value_props_names = value.keys()
         extra_props = set(value_props_names) - set(all_props_names)
-        if extra_props and self.additional_properties is False:
+        extra_props_allowed = self.are_additional_properties_allowed(
+            one_of_schema)
+        if extra_props and not extra_props_allowed:
             raise UndefinedSchemaProperty(extra_props)
 
         if self.additional_properties is not True:
diff --git a/tests/unit/schema/test_schemas.py b/tests/unit/schema/test_schemas.py
index fa608e2..b66dad7 100644
--- a/tests/unit/schema/test_schemas.py
+++ b/tests/unit/schema/test_schemas.py
@@ -711,6 +711,39 @@ class TestSchemaValidate(object):
         with pytest.raises(NoOneOfSchema):
             schema.validate(value)
 
+    @pytest.mark.parametrize('value', [
+        Model({
+            'foo': u("FOO"),
+        }),
+        Model({
+            'foo': u("FOO"),
+            'bar': u("BAR"),
+        }),
+    ])
+    def test_unambiguous_one_of(self, value):
+        one_of = [
+            Schema(
+                'object',
+                properties={
+                    'foo': Schema('string'),
+                },
+                additional_properties=False,
+                required=['foo'],
+            ),
+            Schema(
+                'object',
+                properties={
+                    'foo': Schema('string'),
+                    'bar': Schema('string'),
+                },
+                additional_properties=False,
+                required=['foo', 'bar'],
+            ),
+        ]
+        schema = Schema('object', one_of=one_of)
+
+        schema.validate(value)
+
     @pytest.mark.parametrize('value', [Model(), ])
     def test_object_default_property(self, value):
         schema = Schema('object', default='value1')