Convexity-based measures of shape compactness provide an effective way to identify irregularities in congressional district boundaries. A low convexity coefficient may suggest that a district has been gerrymandered, or it may simply reflect irregularities in the corresponding state boundary. Furthermore, the distribution of population within a district can either amplify or lessen the effects of boundary irregularities. As such, it is essential to take both population data and state boundaries into account when using convexity coefficients to detect gerrymandering. Our boundary-adjusted convexity coefficient provides an efficient way to do so, and it yields results similar to the shortest--path approach taken by Chambers and Miller.