This paper considers bidder behaviour in the United Kingdom's UMTS spectrum auction. Evidence is reviewed which shows that some bidders in this auction did not bid straightforwardly in accordance with fixed valuations of the licenses. We go on to consider more speculative hypotheses about bidders' behaviour, such as the hypotheses that bidders revised their valuations in the light of other bidders' behaviour, or that bidders' valuations of licenses depended on which other companies appeared likely to win a license. We find weak evidence in favor of some of these hypotheses, but no hypothesis is supported by strong direct evidence. We conclude that the rationalization of bidding in the United Kingdom's UMTS auction remains problematic. As a consequence we are cautious regarding the success of the auction in achieving an e.cient allocation of licenses.