Input shaping is an effective means of eliminating vibration in many types of flexible systems. This paper discusses how input shaper performance is affected by a fixed acceleration limit. This type of limit is a common occurrence in many mechanical drive systems because it corresponds to a constant force or torque input. It is shown that some input shapers are not affected by an acceleration limit under certain conditions. A test criterion is developed to determine what types of input shapers are negatively affected, and a method is proposed to compensate for the detrimental effects of the constant acceleration limit. Experimental results from an industrial crane support the main theoretical results.