It is now common knowledge that locally well defined BGP routing policies can interact to produce unexpected routing anomalies globally. We introduce a new class of such problems, called BGP Wedgies. A BGP Wedgie is defined as a policy interaction where (1) there are multiple solutions (routings) at the AS level, (2) some solutions are intended, while others are not, (3) getting stuck in an unintended solution requires resetting BGP sessions to "kick the system" back to an intended solution, (4) no one group of network operators has control over the set of sessions that needs to be reset, and (5) no one set of network operators has enough global knowledge to know what is happening. In such a situation the routing is "wedged" into a local optimum that is very difficult to change. Realistic examples will be given.