diff --git a/swh/storage/algos/snapshot.py b/swh/storage/algos/snapshot.py
--- a/swh/storage/algos/snapshot.py
+++ b/swh/storage/algos/snapshot.py
@@ -169,9 +169,11 @@
 
 def snapshot_resolve_alias(
     storage: StorageInterface, snapshot_id: Sha1Git, alias_name: bytes
-) -> Optional[Tuple[List[SnapshotBranch], Optional[SnapshotBranch]]]:
+) -> Optional[SnapshotBranch]:
     """
-    Resolve snapshot branch alias to its real target.
+    Transitively resolve snapshot branch alias to its real target, and return it;
+    ie. follows every branch that is an alias, until a branch that isn't an alias
+    is found.
 
     Args:
         storage: Storage instance
@@ -179,13 +181,9 @@
         alias_name: name of the branch alias to resolve
 
     Returns:
-        A tuple whose first member is the list of followed branches until the alias
-        got resolved to a branch whose target type is not an alias, and second member
-        the real targeted branch.
-        If a dangling branch is encountered during the resolve process, second member of
-        the tuple will be None.
-        If the target type of the tuple second member is an alias, it means that
-        a cycle has been detected during the resolve process.
+        The first branch that isn't an alias, in the alias chain; or None if
+        there is no such branch (ie. either because of a cycle alias, or a dangling
+        branch).
     """
     snapshot = storage.snapshot_get_branches(
         snapshot_id, branches_from=alias_name, branches_count=1
@@ -194,19 +192,15 @@
         return None
 
     if alias_name not in snapshot["branches"]:
-        return ([], None)
+        return None
 
     last_branch = snapshot["branches"][alias_name]
-    branches = []
-
     seen_aliases = {alias_name}
 
-    while (
-        last_branch is not None
-        and last_branch.target_type == TargetType.ALIAS
-        and last_branch.target not in seen_aliases
-    ):
-        branches.append(last_branch)
+    while last_branch is not None and last_branch.target_type == TargetType.ALIAS:
+        if last_branch.target in seen_aliases:
+            return None
+
         alias_target = last_branch.target
         snapshot = storage.snapshot_get_branches(
             snapshot_id, branches_from=alias_target, branches_count=1
@@ -215,4 +209,4 @@
         last_branch = snapshot["branches"].get(alias_target)
         seen_aliases.add(alias_target)
 
-    return (branches, last_branch)
+    return last_branch
diff --git a/swh/storage/tests/algos/test_snapshot.py b/swh/storage/tests/algos/test_snapshot.py
--- a/swh/storage/tests/algos/test_snapshot.py
+++ b/swh/storage/tests/algos/test_snapshot.py
@@ -279,7 +279,7 @@
     snapshot = Snapshot(branches={})
     swh_storage.snapshot_add([snapshot])
 
-    assert snapshot_resolve_alias(swh_storage, snapshot.id, b"HEAD") == ([], None)
+    assert snapshot_resolve_alias(swh_storage, snapshot.id, b"HEAD") is None
 
 
 def test_snapshot_resolve_alias(swh_storage, sample_data):
@@ -321,27 +321,16 @@
     )
     swh_storage.snapshot_add([snapshot])
 
-    for alias_name, expected_branches in (
-        (rev_alias1_name, ([rev_alias1_branch_info], rev_branch_info)),
-        (
-            rev_alias2_name,
-            ([rev_alias2_branch_info, rev_alias1_branch_info], rev_branch_info),
-        ),
-        (
-            rev_alias3_name,
-            (
-                [
-                    rev_alias3_branch_info,
-                    rev_alias2_branch_info,
-                    rev_alias1_branch_info,
-                ],
-                rev_branch_info,
-            ),
-        ),
-        (rel_alias_name, ([rel_alias_branch_info], rel_branch_info)),
+    for alias_name, expected_branch in (
+        (rev_alias1_name, rev_branch_info),
+        (rev_alias2_name, rev_branch_info,),
+        (rev_alias3_name, rev_branch_info,),
+        (rel_alias_name, rel_branch_info),
     ):
-        branches = snapshot_resolve_alias(swh_storage, snapshot.id, alias_name)
-        assert branches == expected_branches
+        assert (
+            snapshot_resolve_alias(swh_storage, snapshot.id, alias_name)
+            == expected_branch
+        )
 
 
 def test_snapshot_resolve_alias_dangling_branch(swh_storage):
@@ -357,8 +346,7 @@
     )
     swh_storage.snapshot_add([snapshot])
 
-    branches = snapshot_resolve_alias(swh_storage, snapshot.id, alias_name)
-    assert branches == ([alias_branch], None)
+    assert snapshot_resolve_alias(swh_storage, snapshot.id, alias_name) is None
 
 
 def test_snapshot_resolve_alias_missing_branch(swh_storage):
@@ -372,8 +360,7 @@
     snapshot = Snapshot(id=b"42" * 10, branches={alias_name: alias_branch,})
     swh_storage.snapshot_add([snapshot])
 
-    branches = snapshot_resolve_alias(swh_storage, snapshot.id, alias_name)
-    assert branches == ([alias_branch], None)
+    assert snapshot_resolve_alias(swh_storage, snapshot.id, alias_name) is None
 
 
 def test_snapshot_resolve_alias_cycle_found(swh_storage):
@@ -405,8 +392,4 @@
     )
     swh_storage.snapshot_add([snapshot])
 
-    branches = snapshot_resolve_alias(swh_storage, snapshot.id, alias1_name)
-    assert branches == (
-        [alias1_branch_info, alias2_branch_info, alias3_branch_info],
-        alias4_branch_info,
-    )
+    assert snapshot_resolve_alias(swh_storage, snapshot.id, alias1_name) is None