One of the major problems in formal epistemology is the difficulty of combining probabilistic and full (dichotomous, all-or-nothing) beliefs in one and the same formal framework. Major properties of actual human belief systems, including how they are impacted by our cognitive limitations, are used to introduce a series of desiderata for realistic models of such belief systems. This leads to a criticism of previous attempts to combine representations of both probabilistic and full beliefs in one and the same formal model. Furthermore, a formal model is presented in which this is done differently. One of its major features is that contingent propositions can be transferred in both directions between full beliefs and lower degrees of belief, in a way that mirrors real-life acquisitions and losses of full beliefs. The subsystem consisting of full beliefs has a pattern of change that constitutes a credible system of dichotomous belief change.