diff --git a/marshmallow_jsonschema/validation.py b/marshmallow_jsonschema/validation.py
index e0a9c9b..d38c818 100644
--- a/marshmallow_jsonschema/validation.py
+++ b/marshmallow_jsonschema/validation.py
@@ -53,7 +53,7 @@ def handle_length(schema, field, validator, parent_schema):
 
 def handle_one_of(schema, field, validator, parent_schema):
     """Adds the validation logic for ``marshmallow.validate.OneOf`` by setting
-    the JSONSchema `enum` property to the allowed choices in the validator.
+    the JSONSchema `oneOf` property to the allowed choices in the validator.
 
     Args:
         schema (dict): The original JSON schema we generated. This is what we
@@ -69,8 +69,23 @@ def handle_one_of(schema, field, validator, parent_schema):
         dict: New JSON Schema that has been post processed and
             altered.
     """
-    schema["enum"] = list(validator.choices)
-    schema["enumNames"] = list(validator.labels)
+    if schema["type"] not in ["string", "number"]:
+        return schema
+
+    if "oneOf" in schema:
+        return schema
+
+    choices = [
+        field._serialize(choice, field.name, None) for choice in validator.choices
+    ]
+    if not choices:
+        return schema
+
+    labels = validator.labels if validator.labels else choices
+    schema["oneOf"] = [
+        {"type": schema["type"], "title": label, "const": choice}
+        for choice, label in zip(choices, labels)
+    ]
 
     return schema
 
diff --git a/tests/test_dump.py b/tests/test_dump.py
index bfb5db6..151753c 100644
--- a/tests/test_dump.py
+++ b/tests/test_dump.py
@@ -412,8 +412,10 @@ class TestSchema(Schema):
     dumped = validate_and_dump(schema)
 
     assert dumped["definitions"]["TestSchema"]["properties"]["foo"] == {
-        "enum": [v for v in mapping.values()],
-        "enumNames": [k for k in mapping.keys()],
+        "oneOf": [
+            {"type": "number", "title": k, "const": v}
+            for k, v in zip(mapping.keys(), mapping.values())
+        ],
         "format": "integer",
         "title": "foo",
         "type": "number",
diff --git a/tests/test_validation.py b/tests/test_validation.py
index 96d7bec..9a72e20 100644
--- a/tests/test_validation.py
+++ b/tests/test_validation.py
@@ -40,17 +40,11 @@ def test_one_of_validator():
 
     dumped = validate_and_dump(schema)
 
-    assert dumped["definitions"]["UserSchema"]["properties"]["sex"]["enum"] == [
-        "male",
-        "female",
-        "non_binary",
-        "other",
-    ]
-    assert dumped["definitions"]["UserSchema"]["properties"]["sex"]["enumNames"] == [
-        "Male",
-        "Female",
-        "Non-binary/fluid",
-        "Other",
+    assert dumped["definitions"]["UserSchema"]["properties"]["sex"]["oneOf"] == [
+        {"type": "string", "title": "Male", "const": "male"},
+        {"type": "string", "title": "Female", "const": "female"},
+        {"type": "string", "title": "Non-binary/fluid", "const": "non_binary"},
+        {"type": "string", "title": "Other", "const": "other"},
     ]
 
 
@@ -63,8 +57,35 @@ class TestSchema(Schema):
     dumped = validate_and_dump(schema)
 
     foo_property = dumped["definitions"]["TestSchema"]["properties"]["foo"]
-    assert foo_property["enum"] == []
-    assert foo_property["enumNames"] == []
+    assert "oneOf" not in foo_property
+
+
+def test_one_of_object():
+    class TestSchema(Schema):
+        foo = fields.Dict(validate=OneOf([{"a": 1}]))
+
+    schema = TestSchema()
+
+    dumped = validate_and_dump(schema)
+
+    foo_property = dumped["definitions"]["TestSchema"]["properties"]["foo"]
+    assert "oneOf" not in foo_property
+
+
+def test_one_of_custom_field():
+    class CustomField(fields.String):
+        def _jsonschema_type_mapping(self):
+            return {"type": "string", "oneOf": [{"const": "one"}, {"const": "two"}]}
+
+    class TestSchema(Schema):
+        foo = CustomField(validate=OneOf(["one", "two"]))
+
+    schema = TestSchema()
+
+    dumped = validate_and_dump(schema)
+
+    foo_property = dumped["definitions"]["TestSchema"]["properties"]["foo"]
+    assert foo_property["oneOf"] == [{"const": "one"}, {"const": "two"}]
 
 
 @pytest.mark.skipif(MARSHMALLOW_3, reason="marshmallow 2 only")