In the midsession reversal task, choice of one stimulus (S1) is correct for the first half of each session and choice of the other stimulus (S2) is correct for the last half of each session. Although humans and rats develop very close to what has been called a win-stay/lose-shift response strategy, pigeons do not. Pigeons start choosing S2 before the reversal, making anticipatory errors, and they keep choosing S1 after the reversal, making perseverative errors. Research suggests that the pigeons are timing the reversal from the start of the session. However, making the reversal unpredictable does not discourage the pigeons from timing. Curiously, pigeons’ accuracy improves if one decreases the value of the S2 stimulus relative to the S1 stimulus. Another form of asymmetry between S1 and S2 can be found by varying, over trials, the number of S1 or S2 stimuli. Counterintuitively, if the number of S2 stimuli varies, it results in a large increase in anticipatory errors but little increase in perseverative errors. However, if the number of S1 stimuli varies over trials, it results in a large increase in perseverative errors but no increase in anticipatory errors. These last two effects suggest that in the original midsession reversal task, the pigeons are learning to reject S2 during the first half of each session and learning to reject S1 during the last half of each session. These results suggest that reject learning may also play an important role in the learning of simple simultaneous discriminations.