The distribution of the allophones of /?/in certain contexts involves free variation and gradient preferences. An organized survey was conducted to elicit the judgments of 37 native Persian speakers concerning the well-formedness of /?/allophonic behavior in five different phonological positions. The results showed that the differences in judgment between the various categories are not just the result of random variations, but are an authentic reflection of the underlying structural differences. Following Boersma and Hayes (1999) and Hayes (2000), a stochastic model is proposed within optimality theory to account for the gradient judgments involved. The model assumes that constraints are arranged along a continuum of constraint strictness, with a band of strictness value assigned to each. When the strictness bands of two constraints overlap, then both rankings of the two constraints are equally available for the generation of outputs, yielding free variant forms. However, when a particular form can be generated only by assigning a constraint a strictness value (/?/ or /??/) within a designated “fringe” of the strictness band, the model generates the form marked with an intermediate degree of well-formedness.