diff --git a/tests/test_trace.py b/tests/test_trace.py
index cdb7c3e..485b7bb 100644
--- a/tests/test_trace.py
+++ b/tests/test_trace.py
@@ -205,6 +205,25 @@ def user(content, **flags):
     assert trace.claude_prompt_count(p) == 3
 
 
+def test_a_claude_background_task_notification_is_no_prompt(tmp_path):
+    """Claude Code tells the model that a background task finished in a `user` entry of its
+    own, `origin.kind` "task-notification" (2.1.317). The person typed one prompt here. The
+    notification still starts a turn of its own: the model answers it."""
+    note = {"type": "user", "promptSource": "system", "turnOrigin": "task_notification",
+            "origin": {"kind": "task-notification", "producer": "session-task"},
+            "message": {"role": "user", "content": (
+                "<task-notification>\n<task-id>b1</task-id>\n<status>completed</status>\n"
+                "<summary>Background command \"pytest\" completed (exit code 0)</summary>\n"
+                "</task-notification>")}}
+    p = _jsonl(tmp_path / "c.jsonl", [
+        {"type": "user", "message": {"role": "user", "content": "run the tests in the background"}},
+        {"type": "assistant", "message": {"role": "assistant", "content": "started"}},
+        note,
+        {"type": "assistant", "message": {"role": "assistant", "content": "they pass"}}])
+    assert trace.claude_prompt_count(p) == 1
+    assert len(list(trace.claude_prompt_turns(p))) == 2
+
+
 def test_a_codex_session_counts_one_prompt_per_turn(tmp_path):
     turn = [{"type": "turn_context", "payload": {"turn_id": "t"}},
             {"type": "event_msg", "payload": {"type": "task_started"}},
diff --git a/tokeneconomizer/trace/claude.py b/tokeneconomizer/trace/claude.py
index 04f7bb0..ea79b13 100644
--- a/tokeneconomizer/trace/claude.py
+++ b/tokeneconomizer/trace/claude.py
@@ -88,15 +88,23 @@ def _is_prompt(ev):
                                                                 "[Request interrupted"))
 
 
+def _is_notification(ev):
+    """Is this entry Claude Code telling the model that a background task finished? It starts a
+    turn, as a prompt does, but nobody typed it (2.1.317: `origin.kind` "task-notification")."""
+    origin = ev.get("origin")
+    return isinstance(origin, dict) and origin.get("kind") == "task-notification"
+
+
 def claude_prompt_count(transcript_path):
-    """How many prompts the person gave a Claude Code session (`_is_prompt`)."""
+    """How many prompts the person gave a Claude Code session (`_is_prompt`, less the
+    background-task notifications)."""
     n = 0
     for line in _lines(transcript_path):
         try:
             ev = json.loads(line)
         except ValueError:
             continue
-        n += isinstance(ev, dict) and _is_prompt(ev)
+        n += isinstance(ev, dict) and _is_prompt(ev) and not _is_notification(ev)
     return n