Many general range query schemes for DHT-based peer-to-peer (P2P) systems have been proposed, which do not need to modify the underlying DHTs. However, most existing works have the query delay depending on both the scale of the system and the size of the query space or the specific query, and thus cannot guarantee to return the query results in a bounded delay. In this paper, we propose Armada, an efficient general range query scheme to support single-attribute and multipleattribute range queries. Armada is the first delaybounded range query scheme over constant-degree DHTs, and can return the results for any range query within 2logN hops in a P2P system with N peers. Results of analysis and simulations show that the average delay of Armada is less than logN, and the average message cost of single-attribute range queries is about logN+2n..2 (n is the number of peers that intersect with the query). These results are very close to the lower bounds on delay and message cost of range queries over constant-degree DHTs.