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This paper describes an experiment investigating for the first time, the perceptual tolerance of inconsistent projections when rotated billboards are transformed and included in an image among other objects produced by traditional 3D computer graphics. The need for this results has arisen in building a system to assist artists with simultaneous composition in two and three dimensions. Imitating the cartoon-based compositional practices of Renaissance artists we are using billboards as modelling primitives, with the additional freedom of manipulating them in three dimensions rather than two. Three-dimensional manipulation adds the capability of rotating billboards about vertical axes, which introduces geometric distortions exactly like those produced by multiple projections in Renaissance painting. An experiment measured the limits of acceptable distortion by having subjects choose the distorted object from an array of undistorted ones. The results include a concrete limit for acceptable billboard rotations, an identification of object features that create exceptional limits to rotation, and some conclusions about the relationship of canonical views to billboard use.