diff --git a/swh/loader/git/loader.py b/swh/loader/git/loader.py
--- a/swh/loader/git/loader.py
+++ b/swh/loader/git/loader.py
@@ -14,7 +14,6 @@
 
 import dulwich.client
 from dulwich.errors import GitProtocolError, NotGitRepository
-from dulwich.object_store import ObjectStoreGraphWalker
 from dulwich.objects import ShaFile
 from dulwich.pack import PackData, PackInflater
 
@@ -61,13 +60,7 @@
             self.base_snapshots = []
 
         self.heads: Set[HexBytes] = set()
-
-    def get_parents(self, commit: bytes) -> List[bytes]:
-        """This method should return the list of known parents"""
-        return []
-
-    def graph_walker(self) -> ObjectStoreGraphWalker:
-        return ObjectStoreGraphWalker(self.heads, self.get_parents)
+        self.__iterator = None
 
     def determine_wants(self, refs: Dict[bytes, HexBytes]) -> List[HexBytes]:
         """Get the list of bytehex sha1s that the git loader should fetch.
@@ -120,6 +113,15 @@
             )
         return wanted_refs
 
+    # Compatibility with the dulwich graph walker
+    def __next__(self):
+        if not self.__iterator:
+            self.__iterator = iter(self.heads)
+        return next(self.__iterator, None)
+
+    def ack(self, sha):
+        pass
+
 
 @dataclass
 class FetchPackReturn:
@@ -223,7 +225,7 @@
         pack_result = client.fetch_pack(
             path,
             base_repo.determine_wants,
-            base_repo.graph_walker(),
+            base_repo,
             do_pack,
             progress=do_activity,
         )
diff --git a/swh/loader/git/tests/test_loader.py b/swh/loader/git/tests/test_loader.py
--- a/swh/loader/git/tests/test_loader.py
+++ b/swh/loader/git/tests/test_loader.py
@@ -557,6 +557,56 @@
             call("git_known_refs_percent", "h", expected_git_known_refs_percent, {}, 1),
         ]
 
+    def test_load_incremental_negotiation(self):
+        """Check that the packfile negotiated when running an incremental load only
+        contains the "new" commits, and not all objects."""
+
+        snapshot_id = b"\x01" * 20
+        now = datetime.datetime.now(tz=datetime.timezone.utc)
+
+        def ovgl(origin_url, allowed_statuses, require_snapshot, type):
+            if origin_url == f"base://{self.repo_url}":
+                return OriginVisit(origin=origin_url, visit=42, date=now, type="git")
+            else:
+                return None
+
+        self.loader.storage.origin_visit_get_latest.side_effect = ovgl
+        self.loader.storage.origin_visit_status_get_latest.return_value = (
+            OriginVisitStatus(
+                origin=f"base://{self.repo_url}",
+                visit=42,
+                snapshot=snapshot_id,
+                date=now,
+                status="full",
+            )
+        )
+        self.loader.storage.snapshot_get_branches.return_value = {
+            "id": snapshot_id,
+            "branches": {
+                b"refs/heads/master": SnapshotBranch(
+                    # id of the initial commit in the git repository fixture
+                    target=b"\xb6\xf4\x02\x92\xc4\xe9J\x8f~{J\xffP\xe6\xc7B\x9a\xb9\x8e*",
+                    target_type=TargetType.REVISION,
+                ),
+            },
+            "next_branch": None,
+        }
+
+        res = self.loader.load()
+        assert res == {"status": "eventful"}
+
+        stats = get_stats(self.loader.storage)
+        assert stats == {
+            "content": 3,  # instead of 4 for the full repository
+            "directory": 6,  # instead of 7
+            "origin": 1,
+            "origin_visit": 1,
+            "release": 0,
+            "revision": 6,  # instead of 7
+            "skipped_content": 0,
+            "snapshot": 1,
+        }
+
 
 class DumbGitLoaderTestBase(FullGitLoaderTests):
     """Prepare a git repository to be loaded using the HTTP dumb transfer protocol."""