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The equilibrium in the standard New Keynesian (NK) model with Calvo-pricing becomes ex­plosive at low levels of trend inflation (between 4 to 7 percent). Even halfway before that threshold, optimal prices, price dispersion and costs rise fast to very large levels, and output plummets. We show that the root of these issues is not Calvo pricing as commonly assumed, but rather its in­teraction with the popular Dixit-Stiglitz demand structure in NK models. Considering models with general firms’ demand functions and Calvo pricing, we show that the condition for NK mod­els to always have a stable equilibrium, independently of the level of trend inflation, is that the demand function does not increase unboundedly as relative prices decrease. The Dixit-Stiglitz de­mand structure fails to satisfy the latter condition. We then propose a model with price wedges to augment any existing demand structure and make them in line with those conditions. Using Dixit-Stiglitz and Kimball-demand aggregators, we show that the generalized NK model with price wedges allows price dispersion to rise slowly with trend inflation and avoids output plummeting to zero. In addition, the demand function with price wedges has relatively superior properties, better aligned with the micro and macro evidence. Using the generalized model, we show new implications for the slope of the Phillips curve and the effects of monetary shocks.