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 relationship with a neighboring ISP), operators need to change the configuration of the network. Due to the complexity of the Border Gateway Protocol (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 that guarantees no packet loss. Unfortunately, finding such an operational ordering, when it exists, is computationally hard. To enable lossless reconfigurations, we propose a framework that extends current features of carrier-grade routers to run two BGP control planes in parallel. We present a prototype implementation and show the effectiveness of our framework through a case study.