A document-handling apparatus and method for transporting documents along a document feed path from an upstream end to a downstream end. The apparatus includes at least one document-handling subassembly along the document feed path for singulating the documents, controlling gaps between the documents, and conveying the documents toward the downstream end; a sensor mounted along the document feed path for sensing the positions of the documents and for generating position signals based on the document positions; and a control apparatus for receiving the position signals and for controlling the velocity and acceleration of the document-handling subassembly so as to regulate the size of the document gaps and to maximize document throughput. The document-handling subassemblies can include a stack advance mechanism, an input feeder, one or more singulators, and one or more output feeders. A trap can also be included to stop a document along the feed path. The apparatus can operate at accelerations as low as 0.5 g, enabling documents to be transported with constant motion through the apparatus, thereby maintaining efficient inter-document gaps without using high accelerations.