The substantial control premium typically observed in corporate takeovers makes a compelling case for acquiring target shares (a toehold) in the market prior to launching a bid. Moreover, auction theory suggests that toehold bidding may yield a competitive advantage over rival bidders. Nevertheless, with a sample exceeding 10,000 initial control bids for US public targets, we show that toehold bidding has declined steadily since the early 1980s and is now surprisingly rare. At the same time, the average toehold is large when it occurs (20%), and toeholds are the norm in hostile bids. To explain these puzzling observations, we develop and test a two-stage takeover model where attempted merger negotiations are followed by open auction. With optimal bidding, a toehold imposes a cost on target management, causing some targets to (rationally) reject merger negotiations. Optimal toeholds are therefore either zero (to avoid rejection costs) or greater than a threshold (so that toehold benefits offset rejection costs). The toehold threshold estimate averages 9% across initial bidders, reflecting in part the bidder's opportunity loss of a merger termination agreement. In the presence of market liquidity costs, a threshold of this size may well induce a broad range of bidders to select zero toehold. As predicted, the probability of toehold bidding decreases, and the toehold size increases, with the threshold estimate. The model also predicts a relatively high frequency of toehold bidding in hostile bids, as observed. Overall, our test results are consistent with rational bidder behavior with respect to the toehold decision.