diff --git a/api/compression_continuation.py b/api/compression_continuation.py
index 57d69974..64bc7dca 100644
--- a/api/compression_continuation.py
+++ b/api/compression_continuation.py
@@ -10,6 +10,12 @@ from pathlib import Path
 logger = logging.getLogger(__name__)
 
 
+def _is_local_interactive_persisted_source(source):
+    return isinstance(source, str) and source in {
+        "webui", "tui", "cli", "desktop", "acp",
+    }
+
+
 def durable_compression_continuation(session):
     """Return (sealed, resumable tip), without making a recovery write.
 
@@ -49,7 +55,7 @@ def durable_compression_continuation(session):
         if not tip or tip == sid:
             return True, None
         child = db.get_session(tip)
-        if not child or child.get("source") not in {"webui", "tui", "cli"}:
+        if not child or not _is_local_interactive_persisted_source(child.get("source")):
             return True, None
         for row in (parent, child):
             if row.get("profile_name") not in (None, "", profile):
diff --git a/tests/test_compressed_idle_resume.py b/tests/test_compressed_idle_resume.py
index 3dbb0ae2..23cc1c3b 100644
--- a/tests/test_compressed_idle_resume.py
+++ b/tests/test_compressed_idle_resume.py
@@ -49,8 +49,7 @@ class Handler:
         pass
 
 
-def test_stale_post_rejected_before_workspace_or_worker_mutation(lineage, monkeypatch):
-    _, session = lineage
+def _assert_stale_post_rotation(session, monkeypatch, expected_continuation):
     monkeypatch.setattr(routes, "_agent_runtime_barrier_response", lambda **kw: None)
     monkeypatch.setattr(routes, "_get_or_materialize_session", lambda *a, **kw: session)
     monkeypatch.setattr(routes, "_get_active_profile_name", lambda: "default")
@@ -61,7 +60,41 @@ def test_stale_post_rejected_before_workspace_or_worker_mutation(lineage, monkey
     assert h.status == 409
     payload = json.loads(h.wfile.getvalue())
     assert payload["code"] == "session_rotated"
-    assert payload["continuation_session_id"] == "idlechild"
+    assert payload["continuation_session_id"] == expected_continuation
+
+
+def test_stale_post_rejected_before_workspace_or_worker_mutation(lineage, monkeypatch):
+    _, session = lineage
+    _assert_stale_post_rotation(session, monkeypatch, "idlechild")
+
+
+@pytest.mark.parametrize("source", ["desktop", "acp"])
+def test_same_source_local_interactive_lineage_resumes(lineage, monkeypatch, source):
+    db, session = lineage
+    db._conn.execute(
+        "UPDATE sessions SET source=? WHERE id IN ('sealedparent', 'idlechild')",
+        (source,),
+    )
+    db._conn.commit()
+
+    assert routes._pre_compression_continuation_session_id(session) == "idlechild"
+    _assert_stale_post_rotation(session, monkeypatch, "idlechild")
+
+
+@pytest.mark.parametrize(
+    "source",
+    ["cron", "webhook", "kanban", "tool", "subagent", "unknown-source"],
+)
+def test_noninteractive_lineage_is_not_resumable(lineage, monkeypatch, source):
+    db, session = lineage
+    db._conn.execute(
+        "UPDATE sessions SET source=? WHERE id IN ('sealedparent', 'idlechild')",
+        (source,),
+    )
+    db._conn.commit()
+
+    assert routes._pre_compression_continuation_session_id(session) is None
+    _assert_stale_post_rotation(session, monkeypatch, None)
 
 
 def test_idle_tip_accepts_normal_persistence_without_reopening_parent(lineage):