Speculations about whether strategic voting made a difference to the outcome of an election regularly whip up the passions of pundits, party strategists, electoral reformers and scholars alike. Yet, research on strategic voting's political effect has been hampered by the scarcity of data on district level party preferences. We propose the use of Bayesian small area estimation to predict district level preferences from just a handful of survey responses per district and comparing these predictions against election results to estimate how many voters switched sides in each district. We apply the approach to estimate how many seats changed hands as a result of strategic voting at the 1997 and 2001 UK general elections. Despite similar rates of strategic voting in both elections, the number of seats that were affected was markedly greater in 1997. Interestingly, the Liberal Democrats turn out to win the most seats because of strategic voting. We also estimate how many votes went in the ‘wrong’ direction—away from otherwise viable candidates. We validate our results by using journalistic sources and compare them with previous published estimates.