Most peer-to-peer (P2P) overlays based on distributed hash tables (DHTs) focus on stationary Internet hosts. However, when nodes in the last-mile wireless extension are allowed to join the overlay, we will face immediately the problem of peer mobility. That is, when a peer moves to a new location in the network, all the state information regarding the moving peer will become stale, resulting in creating mobility churn to the system in addition to ordinary churn due to peers joining, departure and failure. The paper extensively investigates the performance of a DHT that is operated under mobility churn. The DHT relies on rudimentary failure detection/recovery mechanisms and peer dynamic joining/departure algorithms to handle peer mobility. We show that when compared with an ideal design, rudimentary failure handling mechanisms and peer dynamics processing algorithms often take unhelpful maintenance bandwidth. The rudimentary implementation has fair performance results when ordinary churn rate and/or route request rate is tremendously high.