BGP reconvergence events involving a large number of prefixes may result in the loss of large amounts of traffic. Based on the observation that a very small number of prefixes carries the vast majority of traffic, we propose Power Prefixes Prioritization (PPP) to ensure the routes of these popular BGP prefixes converge first. By doing so, we significantly reduce the amount of traffic lost during reconvergence events. To achieve this, PPP obtains an ordered list of popular prefixes through traffic inspection, and configures the resulting prefix rank in the BGP routers to prioritize the processing and advertisement of BGP routes. We model the benefits of PPP over traditional BGP processing in terms of traffic loss for both generic and a Zipf traffic distribution, and we consider the impact of sampling in the process of obtaining the prefix rank. Applying the mechanism to real traffic traces obtained from WIDE, we show that PPP reduces the amount of traffic lost by an order of magnitude, even when we configure it to use conservative sampling rates. We prototype our proposal in Quagga to show the feasibility of its implementation, and we observe similar traffic loss reduction. PPP can be deployed incrementally, as it is implemented purely as a change in the router-internal BGP processing behavior.