Is centering a stimulus in the field of view an optimal strategy to localize and track it? We demonstrated, through experimental and computational studies, that the answer is no. We trained echolocating Egyptian fruit bats to localize a target in complete darkness, and we measured the directional aim of their sonar clicks. The bats did not center the sonar beam on the target, but instead pointed it off axis, accurately directing the maximum slope ("edge") of the beam onto the target. Information-theoretic calculations showed that using the maximum slope is optimal for localizing the target, at the cost of detection. We propose that the tradeoff between detection (optimized at stimulus peak) and localization (optimized at maximum slope) is fundamental to spatial localization and tracking accomplished through hearing, olfaction, and vision.