diff --git a/README.md b/README.md
index 12e53f8..2ed1339 100644
--- a/README.md
+++ b/README.md
@@ -29,6 +29,8 @@ need this package to have the same functionality.
 
 Here's how `getfullargspec` is different from regular `signature` call:
 
+- the `self` / `cls` parameter is always reported, even for bound methods
+
 ```python
 >>> import inspect
 
@@ -43,13 +45,44 @@ FullArgSpec(args=['self', 'arg'], varargs=None, varkw=None, defaults=None, kwonl
 
 ```
 
+- wrapper chains defined by `__wrapped__` *not* unwrapped automatically
+
+```python
+>>> import functools
+
+>>> def some_decorator(f):
+...     @functools.wraps(f)
+...     def wrapper(*args, **kwargs):
+...         return f(*args, **kwargs)
+...     return wrapper
+
+>>> @some_decorator
+... def func(a: int, /, b: str) -> None: ...
+
+>>> inspect.getfullargspec(func)
+FullArgSpec(args=[], varargs='args', varkw='kwargs', defaults=None, kwonlyargs=[], kwonlydefaults=None, annotations={'return': None})
+
+```
+
 Here's how you can migrate:
 
 ```python
 >>> import inspect313
->>> inspect313.signature(A().method, skip_bound_arg=False)
+
+>>> inspect313.signature(
+...    A().method, 
+...    skip_bound_arg=False, 
+...    follow_wrapped=False,
+... )
 <Signature (self, arg: int) -> None>
 
+>>> inspect313.signature(
+...    func, 
+...    skip_bound_arg=False, 
+...    follow_wrapped=False,
+... )
+<Signature (*args, **kwargs) -> None>
+
 ```
 
 ## License
diff --git a/tests/test_signature.py b/tests/test_signature.py
index 228fc0f..ff66945 100644
--- a/tests/test_signature.py
+++ b/tests/test_signature.py
@@ -1,9 +1,21 @@
+import functools
 import inspect
+from typing import Any, TypeVar, Callable, cast
 
 import pytest
 
 import inspect313
 
+_Func = TypeVar("_Func", bound=Callable[..., Any])
+
+
+def _decorator(func: _Func) -> _Func:
+    @functools.wraps(func)
+    def wrapper(*args: Any, **kwargs: Any) -> Any:
+        return func(*args, **kwargs)
+
+    return cast(_Func, wrapper)
+
 
 def _function(
     a: int,
@@ -18,6 +30,11 @@ def _function(
     """Function to test."""
 
 
+@_decorator  # will have `__wrapped__` set
+def _decorated_function(a: int, /, b: str) -> None:
+    ...
+
+
 class _Class:
     def __init__(self, default: int = 0) -> None:
         ...
@@ -41,6 +58,7 @@ def cl(cls, arg3: int, /, *, arg4: str = "a") -> None:
     "obj",
     [
         _function,
+        _decorated_function,
         _Class,
         _Class(),
         _Class.method,
@@ -66,6 +84,7 @@ def test_signature_default(obj) -> None:
             _function,
             "(a: int, /, b: str, c: int = 0, *d, e: bool, f: bool = True, **kwargs) -> None",
         ),
+        (_decorated_function, "(*args, **kwargs) -> None"),
         (_Class, "(self, default: int = 0) -> None"),
         (_Class(), "(self, c: int, *, d: str) -> None"),
         (_Class.method, "(self, e, /, *args, **kwargs) -> None"),
@@ -76,10 +95,21 @@ def test_signature_default(obj) -> None:
         (_Class().cl, "(cls, arg3: int, /, *, arg4: str = 'a') -> None"),
     ],
 )
-def test_signature_present_bound_arg(obj, expected: str) -> None:
+def test_signature_to_migrate(obj, expected: str) -> None:
     """Test that you keep bound args."""
-    assert str(inspect313.signature(obj, skip_bound_arg=False)) == expected
     assert (
-        str(inspect313.Signature.from_callable(obj, skip_bound_arg=False))
+        str(
+            inspect313.signature(
+                obj, skip_bound_arg=False, follow_wrapped=False
+            )
+        )
+        == expected
+    )
+    assert (
+        str(
+            inspect313.Signature.from_callable(
+                obj, skip_bound_arg=False, follow_wrapped=False
+            )
+        )
         == expected
     )