diff --git a/docs/source/conf.py b/docs/source/conf.py
index 1cc0887e64..06b661f126 100755
--- a/docs/source/conf.py
+++ b/docs/source/conf.py
@@ -80,8 +80,6 @@ def autodoc_process_signature(
     """Modify found signatures to fix various issues."""
     if signature is not None:
         signature = signature.replace("~_contextvars.Context", "~contextvars.Context")
-        if name == "trio.lowlevel.start_guest_run":
-            signature = signature.replace("Outcome", "~outcome.Outcome")
         if name == "trio.lowlevel.RunVar":  # Typevar is not useful here.
             signature = signature.replace(": ~trio._core._local.T", "")
         if "_NoValue" in signature:
diff --git a/trio/_core/_traps.py b/trio/_core/_traps.py
index d7591bb799..e92f5586e9 100644
--- a/trio/_core/_traps.py
+++ b/trio/_core/_traps.py
@@ -11,7 +11,6 @@
 from . import _run
 
 if TYPE_CHECKING:
-    from outcome import Outcome
     from typing_extensions import TypeAlias
 
     from ._run import Task
@@ -182,10 +181,10 @@ def abort(inner_raise_cancel):
 # Not exported in the trio._core namespace, but imported directly by _run.
 @attr.s(frozen=True)
 class PermanentlyDetachCoroutineObject:
-    final_outcome: Outcome[Any] = attr.ib()
+    final_outcome: outcome.Outcome[Any] = attr.ib()
 
 
-async def permanently_detach_coroutine_object(final_outcome: Outcome[Any]) -> Any:
+async def permanently_detach_coroutine_object(final_outcome: outcome.Outcome[Any]) -> Any:
     """Permanently detach the current task from the Trio scheduler.
 
     Normally, a Trio task doesn't exit until its coroutine object exits. When