Resilient Packet Ring (RPR), or the Standard IEEE 802.17, is a new IP-based network technology proposed to replace SONET/SDH in metropolitan area networks. RPR is well-adapted to handle multimedia traffic and is efficient. However, when RPR networks are bridged, inter-ring packets, or packets with the destination on a remote RPR network other than on the source network, are flooded on the source and the destination networks, and also on the path of the intermediate networks between the source and the destination networks. This decreases the available bandwidth for other traffic in those networks and is inefficient. As a result, we propose two solutions based on topology discovery, global topology discovery (GTD) and enhanced topology discovery (ETD), that prevent the flooding of inter-ring packets. GTD enables the bridges to determine the next-hop bridge for each destination. ETD enables the source node to determine a default ringlet, so that packets reach the next-hop bridge without flooding the source network. The proposed solutions were analyzed and the overhead bandwidth and stabilization time were shown to be bounded. Simulations performed showed that the proposed solutions successfully avoid flooding and achieve optimal efficiency in the intermediate and destination networks, and in the source networks with one bridge.