Frequency modulated (FM) halftoning or 'stochastic screening,' has attracted a great deal of attention in the printing industry in recent years. It has several advantages over conventional halftoning. But one serious problem that arises in FM halftoning is dot gain. One approach to stochastic screening uses a specially constructed halftone screen, the blue noise mask (BNM), to produce an unstructured and visually appealing pattern of halftone dots at any gray level. In this paper, we will present methods to correct dot gain with the BNM. Dot gain is related to the area-to-perimeter ration of printed spots. We can exploit this feature in different ways. At a medium level, a B>NM pattern will have 'connected' as well as 'isolated' dots. Normally, as we build down BNM patterns to lower levels, a specific number of white dots will be replace by black dots. Since connected white dots are more likely to be picked than isolated white dots, this will results in substantial dot gain because of the increasing number of isolated white dots. We show that it is possible to constrain the process of constructing a BNM such that isolated dots are preferentially removes, thus significantly reducing dot gain in a BNM.