Decision makers often opt for the deferral outside option when they find it difficult to make an active choice. Contrary to existing logit models with an outside option where the latter is assigned a fixed value exogenously, this paper introduces and analyzes a class of logit models where that option's value is menu-dependent, may be determined endogenously, and could be interpreted as proxying the varying degree of decision difficulty at different menus. We focus on the *power logit* special class of these models. We show that these predict some observed choice-deferral effects that are caused by hard decisions, including non-monotonic "roller-coaster" choice-overload phenomena that are regulated by the presence or absence of a clearly dominant feasible alternative. We illustrate the usability, novel insights and explanatory gains of the proposed framework for empirical discrete choice analysis and theoretical modelling of imperfectly competitive markets in the presence of potentially indecisive consumers.