Z is a formal specification language for describing sequential software systems. As the use of Z increases, the quality of Z specifications as effective means of communication arises. The aim of this paper is to contribute to a systematic assessment of the quality of Z specifications as perceived by their stakeholders. A pragmatic quality framework for Z specifications using notions from semiotics, cognitive psychology, and information system quality is proposed. The goals for pragmatic quality, and manageable criteria and mechanisms to address them in a feasible manner are identified. The utility and trade-offs of the mechanisms in achieving the quality goals of the framework are analyzed. Examples that lead to compromise of pragmatic quality in a Z specification, and techniques for improvement, are given.