Previous research (Whitwell et al. in Exp Brain Res 188:603-611, 2008; Whitwell and Goodale in Exp Brain Res 194:619-629, 2009) has shown that trial history, but not anticipatory knowledge about the presence or absence of visual feedback on an upcoming trial, plays a vital role in determining how that feedback is exploited when grasping with the right hand. Nothing is known about how the non-dominant left hand behaves under the same feedback regimens. In present study, therefore, we compared peak grip aperture (PGA) for left- and right-hand grasps executed with and without visual feedback (i.e., closed- vs. open-loop conditions) in right-handed individuals under three different trial schedules: the feedback conditions were blocked separately, they were randomly interleaved, or they were alternated. When feedback conditions were blocked, the PGA was much larger for open-loop trials as compared to closed-loop trials, although this difference was more pronounced for right-hand grasps than left-hand grasps. Like Whitwell et al., we found that mixing open- and closed-loop trials together, compared to blocking them separately, homogenized the PGA for open- and closed-loop grasping in the right hand (i.e., the PGAs became smaller on open-loop trials and larger on closed-loop trials). In addition, the PGAs for right-hand grasps were entirely determined by trial history and not by knowledge of whether or not visual feedback would be available on an upcoming trial. In contrast to grasps made with the right hand, grasps made by the left hand were affected both by trial history and by anticipatory knowledge of the upcoming visual feedback condition. But these effects were observed only on closed-loop trials, i.e., the PGAs of grasps made with the left hand on closed-loop trials were smaller when participants could anticipate the availability of feedback on an upcoming trial (alternating trials) than when they could not (randomized trials). In contrast, grasps made with the left hand on open-loop trials exhibited the same large PGAs under all feedback schedules: blocked, random, or alternating. In other words, there was no evidence for homogenization. Taken together, these results suggest that in addition to the real-time demands of the task, such as the target's size and position and the availability of visual feedback, the initial (i.e., pre-movement) programming of right-hand grasping relies on what happened on the previous trial, whereas the programming of left-hand grasping is more cognitively supervised and exploits explicit information about trial order to prepare for an upcoming trial.