This paper investigates two central terms in Human Computer Interaction (HCI) – affordances and constraints – and studies their relevance to the design and understanding of digital musical systems. It argues that in the analysis of complex systems, such as new interfaces for musical expression (NIME), constraints are a more productive analytical tool than the common HCI usage of affordances. Constraints are seen as limitations enabling the musician to encapsulate a specific search space of both physical and compositional gestures, proscribing complexity in favor of a relatively simple set of rules that engender creativity. By exploring the design of three different digital musical systems, the paper defines constraints as a core attribute of mapping, whether in instruments or compositional systems. The paper describes the aspiration for designing constraints as twofold: to save time, as musical performance is typically a real-time process, and to minimize the performer’s cognitive load. Finally, it discusses skill and virtuosity in the realm of new musical interfaces for musical expression with regard to constraints.