This paper investigates a subtype of systematic polysemy which in English (and several other languages) appears to rest on the distinction between count and mass uses of nouns (e.g., shoot a rabbit/eat rabbit/wear rabbit). Computational semantic approaches have traditionally analysed such sense alternations as being generated by an inventory of specialised lexical inference rules. The paper puts the central arguments for such a rule-based analysis under scrutiny, and presents evidence that the linguistic component provided by count-mass syntax leaves a more underspecified semantic output than is usually acknowledged by rule-based theories. The paper develops and argues for the positive view that count-mass polysemy is better given a lexical pragmatic analysis, which provides a more flexible and unified account. Treating count-mass syntax as a procedural constraint on NP referents, it is argued that a single, relevance-guided lexical pragmatic mechanism can cover the same ground as lexical rules, as well as those cases in which rule-based accounts need to appeal to pragmatics.