diff --git a/CHANGELOG.md b/CHANGELOG.md
index 47b3f54..74c3ad5 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,7 @@
 # Changelog
 
+- Use a validator that corresponds to the input schema draft version (#66)
+
 #### 0.17.4 - 2020-08-26
 - fixed string schemas with different `format` keywords (#63)
 
diff --git a/src/hypothesis_jsonschema/_canonicalise.py b/src/hypothesis_jsonschema/_canonicalise.py
index 08e3050..b73f169 100644
--- a/src/hypothesis_jsonschema/_canonicalise.py
+++ b/src/hypothesis_jsonschema/_canonicalise.py
@@ -29,6 +29,12 @@
 # (and writing a few steps by hand is a DoS attack on the AST walker in Pytest)
 JSONType = Union[None, bool, float, str, list, Dict[str, Any]]
 Schema = Dict[str, JSONType]
+JSONSchemaValidator = Union[
+    jsonschema.validators.Draft3Validator,
+    jsonschema.validators.Draft4Validator,
+    jsonschema.validators.Draft6Validator,
+    jsonschema.validators.Draft7Validator,
+]
 
 # Canonical type strings, in order.
 TYPE_STRINGS = ("null", "boolean", "integer", "number", "string", "array", "object")
@@ -66,16 +72,19 @@ def next_down(val: float) -> float:
     return out
 
 
-def make_validator(
-    schema: Schema,
-) -> Union[
-    jsonschema.validators.Draft3Validator,
-    jsonschema.validators.Draft4Validator,
-    jsonschema.validators.Draft6Validator,
-    jsonschema.validators.Draft7Validator,
-]:
-    validator_cls = jsonschema.validators.validator_for(schema)
-    return validator_cls(schema)
+def _get_validator_class(schema: Schema) -> JSONSchemaValidator:
+    try:
+        validator = jsonschema.validators.validator_for(schema)
+        validator.check_schema(schema)
+    except jsonschema.exceptions.SchemaError:
+        validator = jsonschema.Draft4Validator
+        validator.check_schema(schema)
+    return validator
+
+
+def make_validator(schema: Schema) -> JSONSchemaValidator:
+    validator = _get_validator_class(schema)
+    return validator(schema)
 
 
 class CanonicalisingJsonEncoder(json.JSONEncoder):
@@ -888,7 +897,7 @@ def merged(schemas: List[Any]) -> Optional[Schema]:
         if out == FALSEY:
             return FALSEY
     assert isinstance(out, dict)
-    jsonschema.validators.validator_for(out).check_schema(out)
+    _get_validator_class(out)
     return out
 
 
diff --git a/tests/test_canonicalise.py b/tests/test_canonicalise.py
index a79bcc4..0cfecf5 100644
--- a/tests/test_canonicalise.py
+++ b/tests/test_canonicalise.py
@@ -521,6 +521,21 @@ def test_canonicalise_is_only_valid_for_schemas():
         canonicalish("not a schema")
 
 
+def test_validators_use_proper_draft():
+    # See GH-66
+    schema = {
+        "$schema": "http://json-schema.org/draft-04/schema#",
+        "not": {
+            "allOf": [
+                {"exclusiveMinimum": True, "minimum": 0},
+                {"exclusiveMaximum": True, "maximum": 10},
+            ]
+        },
+    }
+    cc = canonicalish(schema)
+    jsonschema.validators.validator_for(cc).check_schema(cc)
+
+
 # Expose fuzz targets in a form that FuzzBuzz can understand (no dotted names)
 fuzz_canonical_json_encoding = test_canonical_json_encoding.hypothesis.fuzz_one_input
 fuzz_merge_semantics = test_merge_semantics.hypothesis.fuzz_one_input