Non-Markovian evolution of an open quantum system can be "unraveled" into pure state trajectories generated by a non-Markovian stochastic (diffusive) Schrodinger equation, as introduced by DiÓsi, Gisin, and Strunz. Recently we have shown that such equations can be derived using the modal (hidden variable) interpretation of quantum mechanics. In this paper we generalize this theory to treat jumplike unravelings. To illustrate the jumplike behavior we consider a simple system: a classically driven (at Rabi frequency Ω) two-level atom coupled linearly to a three mode optical bath, with a central frequency equal to the frequency of the atom, ω0, and the two side bands have frequencies ω0′Ω. In the large Ω limit we observed that the jumplike behavior is similar to that observed in this system with a Markovian (broad band) bath. This is expected as in the Markovian limit the fluorescence spectrum for a strongly driven two level atom takes the form of a Mollow triplet. However, the length of time for which the Markovian-like behavior persists depends upon which jumplike unraveling is used. Yes Yes