diff --git a/swh/storage/proxies/buffer.py b/swh/storage/proxies/buffer.py
--- a/swh/storage/proxies/buffer.py
+++ b/swh/storage/proxies/buffer.py
@@ -9,7 +9,7 @@
 from typing_extensions import Literal
 
 from swh.core.utils import grouper
-from swh.model.model import BaseModel, Content, Directory, SkippedContent
+from swh.model.model import BaseModel, Content, Directory, Revision, SkippedContent
 from swh.storage import get_storage
 from swh.storage.interface import StorageInterface
 
@@ -39,6 +39,7 @@
     "directory": 25000,
     "directory_entries": 200000,
     "revision": 100000,
+    "revision_parents": 200000,
     "release": 100000,
     "snapshot": 25000,
     "extid": 10000,
@@ -68,6 +69,7 @@
               directory: 5000
               directory_entries: 100000
               revision: 1000
+              revision_parents: 2000
               release: 10000
               snapshot: 5000
 
@@ -83,6 +85,7 @@
         }
         self._contents_size: int = 0
         self._directory_entries: int = 0
+        self._revision_parents: int = 0
 
     def __getattr__(self, key: str):
         if key.endswith("_add"):
@@ -134,6 +137,17 @@
 
         return stats
 
+    def revision_add(self, revisions: Sequence[Revision]) -> Dict[str, int]:
+        stats = self.object_add(revisions, object_type="revision", keys=["id"])
+
+        if not stats:
+            # We did not flush based on number of objects; check the number of parents
+            self._revision_parents += sum(len(r.parents) for r in revisions)
+            if self._revision_parents >= self._buffer_thresholds["revision_parents"]:
+                return self.flush(["content", "directory", "revision"])
+
+        return stats
+
     def object_add(
         self,
         objects: Sequence[BaseModel],
@@ -196,5 +210,7 @@
                 self._contents_size = 0
             elif object_type == "directory":
                 self._directory_entries = 0
+            elif object_type == "revision":
+                self._revision_parents = 0
 
         self.storage.clear_buffers(object_types)
diff --git a/swh/storage/tests/test_buffer.py b/swh/storage/tests/test_buffer.py
--- a/swh/storage/tests/test_buffer.py
+++ b/swh/storage/tests/test_buffer.py
@@ -359,6 +359,29 @@
     assert s == {}
 
 
+def test_buffering_proxy_storage_revision_parents_threshold(sample_data) -> None:
+    revisions = sample_data.revisions
+    n_parents = sum(len(r.parents) for r in revisions)
+    threshold = sum(len(r.parents) for r in revisions[:-2])
+
+    # ensure the threshold is in the middle
+    assert 0 < threshold < n_parents
+
+    storage = get_storage_with_buffer_config(
+        min_batch_size={"revision_parents": threshold}
+    )
+    storage.storage = Mock(wraps=storage.storage)
+
+    for revision in revisions:
+        storage.revision_add([revision])
+    storage.flush()
+
+    # We should have called the underlying revision_add at least twice, as
+    # we have hit the threshold for number of parents on revision n-2
+    method_calls = Counter(c[0] for c in storage.storage.method_calls)
+    assert method_calls["revision_add"] >= 2
+
+
 def test_buffering_proxy_storage_release_threshold_not_hit(sample_data) -> None:
     releases = sample_data.releases
     threshold = 10