A sheet interleaver is provided for a slicing machine that includes a slicing plane for slicing an elongated food product and a sheet from web material beneath the elongated product. The interleaver includes a supply of web material, a drawing station, a feed station, and a controller. The drawing station has a first driver for drawing web material from the supply. The feed station has a second driver for receiving web material from the drawing station and driving the web material through a cutting nip into the slicing plane. The controller is in signal-communication with at least one of the first and second drivers to drive web material at select differential speeds by the first and second drivers such that tension between the drawing station and the feed station is controlled to allow a slackened length of web material between the drawing station and the feed station.