Prioritized bases, i.e., weakly ordered sets of sentences, have been used for specifying an agent's "basic" or "explicit" beliefs, or alternatively for compactly encoding an agent's belief state without the claim that the elements of a base are in any sense basic. This paper focuses on the second interpretation and shows how a shifting of priorities in prioritized bases can be used for a simple, constructive and intuitive way of representing a large variety of methods for the change of belief states—methods that have usually been characterized semantically by a system-of-spheres modeling. Among the methods represented are "radical", "conservative" and "moderate" revision, "revision by comparison" in its raising and lowering variants, as well as various constructions for belief expansion and contraction. Importantly, none of these methods makes any use of numbers.