Projection-based appearances are used in a variety of computer graphics applications to impart different appearances onto physical surfaces using digitally controlled projector light. To achieve a compliant appearance, all points on the physical surface must be altered to the colours of the desired target appearance; otherwise, an incompliant appearance results in a misleading visualization. Previous systems typically assume to operate with compliant appearances or restrict themselves to the simpler case of white surfaces. To achieve compliancy, one may change the physical surface's albedo, increase the amount of projector light radiance available or modify the target appearance's colours. This paper presents an approach to modify a target appearance to achieve compliant appearance editing without altering the physical surface or the projector setup. Our system minimally alters the target appearance's colours while maintaining cues important for perceptual similarity (e.g. colour constancy). First, we discuss how to measure colour compliancy. Next, we describe our approach to partition the physical surface into patches based on the surface's colours and the target appearance's colours. Finally, we describe our appearance optimization process, which computes a compliant appearance that is as perceptually similar as possible to the target appearance's colours. We perform several real-world projection-based appearances and compare our results to naïve approaches, which either ignore compliancy or simply reduce the appearance's overall brightness.