diff --git a/openapi_to_fastapi/tests/test_router.py b/openapi_to_fastapi/tests/test_router.py
index 8744f61..f9e567d 100644
--- a/openapi_to_fastapi/tests/test_router.py
+++ b/openapi_to_fastapi/tests/test_router.py
@@ -1,4 +1,5 @@
-from typing import Any, Dict
+import inspect
+from typing import Any, Dict, Optional
 
 import pydantic
 import pytest
@@ -596,3 +597,42 @@ def make_strict_request(json: Dict[str, Any]) -> Any:
     assert resp.status_code == expected_strict_code, resp.json()
     if resp.status_code != 200:
         assert json_snapshot == resp.json()
+
+
+def test_modified_handler_signatures(app, client, specs_root):
+
+    spec_router = SpecRouter(specs_root / "definitions")
+
+    def handler_1(request, x_my_header: Optional[str] = Header(None)):
+        return {}
+
+    def handler_2(request, x_my_header: Optional[str] = Header(None)):
+        return {}
+
+    # Remove the header from handler_2
+    sig = inspect.signature(handler_2)
+    params = sig.parameters
+    filtered_params = [
+        param for param_name, param in params.items() if param_name != "x_my_header"
+    ]
+    handler_2.__signature__ = sig.replace(parameters=filtered_params)
+
+    # Add handlers to router (non-decorator syntax)
+    spec_router.post("/TestValidation_v0.1")(handler_1)
+    spec_router.post("/TestValidation_v0.2")(handler_2)
+
+    router = spec_router.to_fastapi_router()
+    app.include_router(router)
+    openapi_spec = app.openapi()
+
+    route_spec_1 = openapi_spec["paths"]["/TestValidation_v0.1"]
+    route_spec_2 = openapi_spec["paths"]["/TestValidation_v0.2"]
+
+    parameters_1 = route_spec_1["post"].get("parameters", {})
+    parameters_2 = route_spec_2["post"].get("parameters", {})
+
+    headers_1 = {p.get("name") for p in parameters_1 if p.get("in") == "header"}
+    headers_2 = {p.get("name") for p in parameters_2 if p.get("in") == "header"}
+
+    assert "x-my-header" in headers_1
+    assert "x-my-header" not in headers_2
diff --git a/openapi_to_fastapi/utils.py b/openapi_to_fastapi/utils.py
index af51b0d..93ef7a4 100644
--- a/openapi_to_fastapi/utils.py
+++ b/openapi_to_fastapi/utils.py
@@ -22,6 +22,11 @@ def copy_function(fn) -> Callable:
     )
     g.__kwdefaults__ = deepcopy(fn.__kwdefaults__)
     g.__annotations__ = deepcopy(fn.__annotations__)
+
+    # Signature is immutable, no need to copy/deepcopy
+    # Mypy doesn't know about __signature__: https://github.com/python/mypy/issues/12472
+    g.__signature__ = inspect.signature(fn)  # type: ignore[attr-defined]
+
     return g
 
 
@@ -32,9 +37,22 @@ def add_annotation_to_first_argument(fn: FunctionType, model: Type[pydantic.Base
     :param fn: Function to patch
     :param model: Type to add to the first argument
     """
-    fn_spec = inspect.getfullargspec(fn)
-    if not len(fn_spec.args):
+
+    sig = inspect.signature(fn)
+    params = sig.parameters
+    if not params:
         raise ValueError(f"Function {fn.__name__} has no arguments")
-    untyped_args = [a for a in fn_spec.args if a not in fn.__annotations__]
-    if untyped_args:
-        fn.__annotations__[untyped_args[0]] = model
+
+    updated = False
+    updated_params = []
+    for param_name, param in params.items():
+        if not updated and param.annotation is inspect.Parameter.empty:
+            updated_params.append(param.replace(annotation=model))
+            updated = True
+        else:
+            updated_params.append(param)
+
+    # Mypy doesn't know about __signature__: https://github.com/python/mypy/issues/12472
+    fn.__signature__ = sig.replace(  # type: ignore[attr-defined]
+        parameters=updated_params
+    )
diff --git a/pyproject.toml b/pyproject.toml
index 3b3f4f3..04ccc94 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,6 +1,6 @@
 [tool.poetry]
 name = "openapi-to-fastapi"
-version = "0.20.0"
+version = "0.21.0"
 description = "Create FastAPI routes from OpenAPI spec"
 authors = ["IOXIO Ltd"]
 license = "BSD-3-Clause"