diff --git a/swh/loader/git/dumb.py b/swh/loader/git/dumb.py
--- a/swh/loader/git/dumb.py
+++ b/swh/loader/git/dumb.py
@@ -102,7 +102,7 @@
                     # commit not already seen in the current load
                     parent not in self.objects[b"commit"]
                     # commit not already archived by a previous load
-                    and parent not in self.base_repo.heads
+                    and parent not in self.base_repo.local_heads
                 ):
                     commit_objects.append(cast(Commit, self._get_git_object(parent)))
                     self.objects[b"commit"].add(parent)
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
@@ -60,14 +60,18 @@
         else:
             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 []
+        # Cache existing heads
+        self.local_heads: Set[HexBytes] = set()
+        heads_logger.debug("Heads known in the archive:")
+        for base_snapshot in self.base_snapshots:
+            for branch_name, branch in base_snapshot.branches.items():
+                if not branch or branch.target_type == TargetType.ALIAS:
+                    continue
+                heads_logger.debug("    %r: %s", branch_name, branch.target.hex())
+                self.local_heads.add(HexBytes(hashutil.hash_to_bytehex(branch.target)))
 
     def graph_walker(self) -> ObjectStoreGraphWalker:
-        return ObjectStoreGraphWalker(self.heads, self.get_parents)
+        return ObjectStoreGraphWalker(self.local_heads, get_parents=lambda commit: [])
 
     def determine_wants(self, refs: Dict[bytes, HexBytes]) -> List[HexBytes]:
         """Get the list of bytehex sha1s that the git loader should fetch.
@@ -84,18 +88,6 @@
             for name, value in refs.items():
                 heads_logger.debug("    %r: %s", name, value.decode())
 
-        heads_logger.debug("Heads known in the archive:")
-        # Cache existing heads
-        local_heads: Set[HexBytes] = set()
-        for base_snapshot in self.base_snapshots:
-            for branch_name, branch in base_snapshot.branches.items():
-                if not branch or branch.target_type == TargetType.ALIAS:
-                    continue
-                heads_logger.debug("    %r: %s", branch_name, branch.target.hex())
-                local_heads.add(HexBytes(hashutil.hash_to_bytehex(branch.target)))
-
-        self.heads = local_heads
-
         # Get the remote heads that we want to fetch
         remote_heads: Set[HexBytes] = set()
         for ref_name, ref_target in refs.items():
@@ -103,9 +95,9 @@
                 continue
             remote_heads.add(ref_target)
 
-        logger.debug("local_heads_count=%s", len(local_heads))
+        logger.debug("local_heads_count=%s", len(self.local_heads))
         logger.debug("remote_heads_count=%s", len(remote_heads))
-        wanted_refs = list(remote_heads - local_heads)
+        wanted_refs = list(remote_heads - self.local_heads)
         logger.debug("wanted_refs_count=%s", len(wanted_refs))
         if self.statsd is not None:
             self.statsd.histogram(
@@ -115,7 +107,7 @@
             )
             self.statsd.histogram(
                 "git_known_refs_percent",
-                len(local_heads & remote_heads) / len(remote_heads),
+                len(self.local_heads & remote_heads) / len(remote_heads),
                 tags={},
             )
         return wanted_refs
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
@@ -26,7 +26,14 @@
     get_stats,
     prepare_repository_from_archive,
 )
-from swh.model.model import Origin, OriginVisit, OriginVisitStatus, Snapshot
+from swh.model.model import (
+    Origin,
+    OriginVisit,
+    OriginVisitStatus,
+    Snapshot,
+    SnapshotBranch,
+    TargetType,
+)
 
 
 class CommonGitLoaderNotFound:
@@ -557,6 +564,56 @@
             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=bytes.fromhex("b6f40292c4e94a8f7e7b4aff50e6c7429ab98e2a"),
+                    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."""