We seek to provide fairly general conditions that may be imposed on parameters in order that any empirical consumer demand system is consistent with utility maximization. In standard demand systems the imposition of these regularity conditions is less essential than in more complex situations, like when there is rationing or when there are endogenously switching regimes. The paper starts out by giving a number of examples where the failure to properly take into account restrictions following from neoclassical theory leads to models that are not internally coherent. Let 0 be the space of parameters which generate internally coherent models. We show that even if the true parameter vector belongs to 0, failure to constrain the parameter estimates to 0 in "maximum likelihood" estimation may yield inconsistent estimates outside of 0. Next a general framework is provided in which it is possible to formulate parameter restrictions which guarantee utility consistent models. For various cases (standard demand systems, rationing, endogenous regimes) we suggest general conditions that can be imposed in order to guarantee coherency of the empirical model. Since random parameter variation is allowed for, to capture non-systematic differences in preferences across individuals, the conditions also imply restrictions on the stochastic specification of an empirical model. For a number of familiar demand systems we show what the parameter restrictions amount to in practice.