diff --git a/pydantic_ai_slim/pydantic_ai/models/openai.py b/pydantic_ai_slim/pydantic_ai/models/openai.py
index dc1026f9f..d6a76de80 100644
--- a/pydantic_ai_slim/pydantic_ai/models/openai.py
+++ b/pydantic_ai_slim/pydantic_ai/models/openai.py
@@ -992,10 +992,18 @@ def walk(self) -> JsonSchema:
     def transform(self, schema: JsonSchema) -> JsonSchema:  # noqa C901
         # Remove unnecessary keys
         schema.pop('title', None)
-        schema.pop('default', None)
         schema.pop('$schema', None)
         schema.pop('discriminator', None)
 
+        default = schema.get('default', _sentinel)
+        if default is not _sentinel:
+            # the "default" keyword is not allowed in strict mode, but including it makes some Ollama models behave
+            # better, so we keep it around when not strict
+            if self.strict is True:
+                schema.pop('default', None)
+            elif self.strict is None:
+                self.is_strict_compatible = False
+
         if schema_ref := schema.get('$ref'):
             if schema_ref == self.root_ref:
                 schema['$ref'] = '#'
diff --git a/tests/models/test_openai.py b/tests/models/test_openai.py
index b19c03b6c..0e3f6fe99 100644
--- a/tests/models/test_openai.py
+++ b/tests/models/test_openai.py
@@ -829,7 +829,10 @@ def tool_with_tuples(x: tuple[int], y: tuple[str] = ('abc',)) -> str:
                     '$defs': {
                         'MyDefaultRecursiveDc': {
                             'properties': {
-                                'field': {'anyOf': [{'$ref': '#/$defs/MyDefaultRecursiveDc'}, {'type': 'null'}]}
+                                'field': {
+                                    'anyOf': [{'$ref': '#/$defs/MyDefaultRecursiveDc'}, {'type': 'null'}],
+                                    'default': None,
+                                }
                             },
                             'type': 'object',
                         },
@@ -947,7 +950,7 @@ def tool_with_tuples(x: tuple[int], y: tuple[str] = ('abc',)) -> str:
                 {
                     '$defs': {
                         'MyDefaultDc': {
-                            'properties': {'x': {'type': 'integer'}},
+                            'properties': {'x': {'default': 1, 'type': 'integer'}},
                             'type': 'object',
                         }
                     },
@@ -987,7 +990,7 @@ def tool_with_tuples(x: tuple[int], y: tuple[str] = ('abc',)) -> str:
                 {
                     '$defs': {
                         'MyDefaultDc': {
-                            'properties': {'x': {'type': 'integer'}},
+                            'properties': {'x': {'default': 1, 'type': 'integer'}},
                             'type': 'object',
                         }
                     },
@@ -1027,7 +1030,7 @@ def tool_with_tuples(x: tuple[int], y: tuple[str] = ('abc',)) -> str:
                 {
                     '$defs': {
                         'MyDefaultDc': {
-                            'properties': {'x': {'type': 'integer'}},
+                            'properties': {'x': {'default': 1, 'type': 'integer'}},
                             'type': 'object',
                         }
                     },