All stratigraphic cyclicity results from cyclic sedimentation; therefore patterns of stratigraphic cyclicity can be interpreted correctly only once cyclic sedimentation has been properly understood. Cyclic sedimentation occurs at any site at which there is cyclic variation in either or both of the two proximate controls on sedimentation: these are sediment budget (here defined as a generalization of sediment supply) and sedimentation capacity (here defined as a generalization of accommodation). Different patterns of cyclic variation in these controls produce different types of sedimentation cycle, which result in different patterns of stratigraphic cyclicity. A quantitative model for cyclic sedimentation suggests that the possible types of sedimentation cycle fall naturally into four families. Of these families, the most difficult to use for reconstructing sedimentation conditions is the "sawtooth" family; sawtooth cyclicity occurs when changing sedimentation conditions prevent stability from ever being reached. The model shows that sequence boundaries in cyclic successions need not be closely tied to inflection points in baselevel curves; sequences can start at any time from shortly after the baselevel null point on a cycle's falling-baselevel limb to shortly before the baselevel high point on a cycle's rising-baselevel limb, i.e., a time range of almost three-quarters of a cycle. The model also suggests that cyclic successions may intrinsically be more complete than noncyclic ones.