The present invention is for an apparatus that receives input data at a non-uniform first data rate carried by a system clock, and provides output data at a substantially uniform second data rate that is nominally equal to the first data rate and is also carried by the system clock. The system clock is faster than the first or second data rates and accordingly, a write enable signal controls the input data that is written into a saturating elastic store and a read enable signal controls the reading and output of data from the saturating elastic store. The saturating elastic store includes a plurality of storage locations and provides a storage fill level indicative of the amount of storage locations currently holding data. A digital filter receives the storage fill level and filters the storage fill level to provide a control word to a digitally controlled read enable signal generator. The digitally controlled read enable signal generator provides a read enable signal that is nominally the second data rate and that can be varied about the nominal second data rate in response to the control word. The digitally controlled read enable signal generator is able to vary the read enable signal rate by providing a plurality of stuff bit opportunities interspersed between the read enable signals. Some of these stuff bit opportunities are filled to set the read enable signal rate at the nominal second data rate value. By filling or not filling the stuff bit opportunities, the read enable signal rate can be adjusted over a narrow band of frequencies.