We explore task tolerances, i.e., allowable position or rotation inaccuracy, as an important resource to facilitate smooth and effective telemanipulation. Task tolerances provide a robot flexibility to generate smooth and feasible motions; however, in teleoperation, this flexibility may make the user's control less direct. In this work, we implemented a telemanipulation system that allows a robot to autonomously adjust its configuration within task tolerances. We conducted a user study comparing a telemanipulation paradigm that exploits task tolerances (functional mimicry) to a paradigm that requires the robot to exactly mimic its human operator (exact mimicry), and assess how the choice in paradigm shapes user experience and task performance. Our results show that autonomous adjustments within task tolerances can lead to performance improvements without sacrificing perceived control of the robot. Additionally, we find that users perceive the robot to be more under control, predictable, fluent, and trustworthy in functional mimicry than in exact mimicry.