We use simple walking models, based on mechanical principles, to study the preferred strategy selection in human stumble recovery. Humans typically apply an elevating strategy in response to a stumble in early swing and midswing, for which the perturbed step is lengthened in a continuation of the original step. A lowering strategy is executed for stumbles occurring at midswing or late swing, for which the perturbed swing foot is immediately placed on the ground and the recovery is executed in the subsequent step. There is no clear understanding of why either strategy is preferred over the other. We hypothesize that the human strategy preference is the result of an attempt to minimize the cost of successful recovery. We evaluate five hypothesized measures for recovery cost, focusing on the energetic cost of active recovery limb placement. We determine all hypothesized cost measures as a function of the chosen recovery strategy and the timing of the stumble during gait. Minimization of the cost measures based on the required torque, impulse, power and torque/time results in a humanlike strategy preference. The cost measure based on swing work does not predict a favorable strategy as a function of the gait phase.