In dynamic MRI, it is often difficult to achieve the acquisition speed required to resolve or freeze the temporal variations of the imaged object. Several MRI methods aim at speeding up the image acquisition process. Through assumptions and/or prior knowledge, these dynamic MRI methods allow part of the needed data to be calculated instead of acquired. For example, partial-Fourier imaging assumes that phase varies smoothly within the object, and parallel imaging (e.g., simultaneous acquisition of spatial harmonics (SMASH) and sensitivity encoding (SENSE)) uses prior knowledge about receiver-coil sensitivity. While these methods accelerate acquisition, they can introduce artifacts or amplify noise in doing so. The present work aims at accelerating image acquisition significantly, while introducing almost no artifacts or noise amplification. It is shown here that new, extra information is gained if dynamic MRI methods are modified so that the sampling function changes in specific ways from time-frame to time-frame. In other words, the set of k-space locations that are acquired (instead of calculated) changes with time. The present temporal strategy, based on the UNaliasing by Fourier-encoding the Overlaps in the temporaL Dimension (UNFOLD) method, can be incorporated into common dynamic MRI methods. Results with partial-Fourier, SMASH, and SENSE imaging are presented here, where UNFOLD's contribution is to very significantly reduce the artifact and/or amplified noise content. Used in this way, UNFOLD contributes indirectly, rather than directly to the improvement in image acquisition speed, as it allows companion methods to operate properly at greater acceleration settings than would otherwise be feasible.