The network infrastructure of Internet Service Providers (ISPs) undergoes constant evolution. Whenever new requirements arise (e.g., the deployment of a new Point of Presence, or a change in the business relationships with a neighboring ISP), operators need to change the configuration of the network. Due to the complexity of BGP, and the lack of methodologies and tools, maintaining service availability during reconfigurations that involve BGP is a challenge for operators. In this paper, we show that the current best practices to reconfigure BGP do not provide guarantees with respect to traffic disruptions. Then, we study the problem of finding an operational ordering of BGP reconfiguration steps which guarantees no packet loss. Unfortunately, such an operational ordering, when it exists, is computationally hard to find. To enable lossless reconfigurations, we propose a framework which extends current features of carrier-grade routers to run two BGP control planes in parallel. We present a prototype implementation and we show the effectiveness of our framework through a case study.