In this paper, we present built-in test pattern generation (TPG) mechanisms that can enforce a prescribed exact set of phaseshifts, or channel separations, on the bit sequences produced by their successive stages, while still requiring low hardware overhead. Such mechanisms are used in controlling the amount of correlations and/or linear dependencies that are problematic for pseudorandom and pseudoexhaustive TPG in a two-dimensional TPG architecture. The reduction in hardware overhead is achieved by a new technique that merges the logic of the original TPG mechanism with that of the required phase shifter network in order to yield an improved compact structure.