Conversations API: PATCH /conversations/conversations/{conversationId}/participants/{participantId} returning 409

Trying to drop a specific leg from a 3-way conference using the Conversations API. Sending a PATCH to /conversations/conversations/{id}/participants/{legId} with {"action": "disconnect"}. It keeps hitting a 409 Conflict. The participant state is connected and I’m the initiator. Any idea why the API refuses the disconnect?