diff --git a/gidgethub/__init__.py b/gidgethub/__init__.py
index a8567ed..396dfe3 100644
--- a/gidgethub/__init__.py
+++ b/gidgethub/__init__.py
@@ -3,7 +3,7 @@
 __version__ = "5.4.0.dev"
 
 import http
-from typing import Any, Optional
+from typing import Any, Mapping, Optional
 
 
 class GitHubException(Exception):
@@ -19,8 +19,14 @@ class ValidationFailure(GitHubException):
 class HTTPException(GitHubException):
     """A general exception to represent HTTP responses."""
 
-    def __init__(self, status_code: http.HTTPStatus, *args: Any) -> None:
+    def __init__(
+        self,
+        status_code: http.HTTPStatus,
+        *args: Any,
+        headers: Optional[Mapping[str, str | None]] = None,
+    ) -> None:
         self.status_code = status_code
+        self.headers = headers or {}
         if args:
             super().__init__(*args)
         else:
diff --git a/gidgethub/sansio.py b/gidgethub/sansio.py
index 95830f6..1c2bead 100644
--- a/gidgethub/sansio.py
+++ b/gidgethub/sansio.py
@@ -377,7 +377,7 @@ def decipher_response(
             args = status_code_enum, message
         else:
             args = (status_code_enum,)
-        raise exc_type(*args)
+        raise exc_type(*args, headers=headers)
 
 
 DOMAIN = "https://api.github.com"
diff --git a/tests/test_sansio.py b/tests/test_sansio.py
index 1139adb..2fbe039 100644
--- a/tests/test_sansio.py
+++ b/tests/test_sansio.py
@@ -416,8 +416,10 @@ def test_422_html_response(self):
     def test_3XX(self):
         status_code = 301
         with pytest.raises(RedirectionException) as exc_info:
-            sansio.decipher_response(status_code, {}, b"")
+            headers = {"location": "https://api.github.com/test"}
+            sansio.decipher_response(status_code, headers, b"")
         assert exc_info.value.status_code == http.HTTPStatus(status_code)
+        assert exc_info.value.headers == headers
 
     def test_2XX_error(self):
         status_code = 205