The trimming problem for swept volumes — concerning the excision of points ostensibly on the boundary that actually lie in the swept volume interior — is investigated in detail. Building upon several techniques that have appeared in the literature, efficient methods for both local and global trimming of swept volume are developed. These methods are shown to be computationally cost effective when combined with the sweep-envelope differential equation algorithm for the approximate calculation and graphical rendering of swept volumes for quite general objects and sweeps. Examples are presented to demonstrate the efficacy of the trimming strategies.