The problem of packet scheduling for traffic streams with target outflow profiles traversing input queued switches is formulated in this paper. Target outflow profiles specify the desirable inter-departure times of packets leaving the switch from each traffic stream. The goal of the switch scheduler is to dynamically select service configurations of the switch, so that actual outflow streams ("pulled" through the switch) adhere to their desired target profiles as accurately as possible.Dynamic service controls (schedules) are developed to minimize deviation of actual outflow streams from their targets and suppress stream "distortion". Using appropriately selected subsets of service configurations of the switch, efficient schedules are designed, which deliver high performance at relatively low complexity. Some of these schedules are provably shown to achieve 100% pull-throughput. Moreover, simulations demonstrate that for even substantial contention of streams through the switch, due to stringent/intense target outflow profiles, the proposed schedules achieve closely their target profiles and suppress stream distortion.The switch model investigated here deviates from the classical switching paradigm. In the latter, the goal of packet scheduling is primarily to "push" as much traffic load through the switch as possible, while controlling delay to traverse the switch and keeping congestion/backlogs from exploding. In the model presented here, however, the goal of packet scheduling is to "pull" traffic streams through the switch, maintaining desirable (target) outflow profiles.