Delivering a transport stream using a hybrid statistical multiplexer. Over a plurality of multiplexing cycles, a plurality of single program transport streams (SPTSs) are multiplexed onto a multiple program transport stream (MPTS). In each multiplexing cycle, it is determined whether any portion of the packets carried by the plurality of SPTSs may be delayed such that the delayed portion is multiplexed onto the MPTS in a future multiplexing cycle. For each multiplexing cycle, delay information that identifies how many packets were delayed is determined. The size of the bit rate pool for a subsequent allocation cycle is adjusted based on the delay information for a prior multiplexing cycle. Thereafter, the MPTS is delivered to one or more recipients.