The determiners many and few are problematic for generalized quantifier theory because, as has frequently been noted, their interpretations are radically context dependent. While other quantificational determiners are also partially dependent upon contextual factors, it is generally possible to specify the context independent component of their interpretations in a precise way. This is not the case with many and few, where there is wide disagreement on how to express the membership condition for the set of sets denoted by an NP of the form ||many/few(A)||. I propose a constraint-based approach to the interpretation of many and few on which the constraints that determine the value of a variable in the meaning schema for these determiners are themselves the value of a parameter in the schema. The proposed account captures the radical vagueness of ||many|| and ||few|| by leaving the constraints which determine the value of a central element in their interpretations unspecified. However, it avoids the proliferation of ambiguities that characterizes the extensional analyses of Barwise and Cooper (1981), Westerstahl (1995), and Lappin (1988) and (1993). These analyses treat the interpretation of ||many|| as a disjunction of specific conditions. Therefore, whenever a new condition is specified to capture another reading, it gives rise to an additional ambiguity in the interpretation of many/few. The account also escapes the difficulties of the intensional treatments suggested in Keenan and Stavi (1986) and Fernando and Kamp (1996). The former implies that symmetry should hold for ||many|| and ||few||. The latter requires the assignment of probability values to possible worlds, and it is not at all clear how one could compute these values in a precise and non-arbitrary way. Moreover, both the intensional and extensional perspectives are overly restrictive in that they exclude a variety of plausible readings. The approach developed here is similar in spirit to that pursued in Reyle (1993), Dalrymple, et al., Copestake et al (1997), and Crouch (forthcoming). On this view semantic interpretations consist of underspecified formal structures, and specific readings are generated by imposing constraints on the values of parametric variables in these structures.