Iterative source-channel decoding (ISCD) exploits the residual redundancy of source codec parameters by using the Turbo principle. In this paper we extend the excellent capabilities of ISCD to a hybrid automatic repeat request (HARQ) scheme by novel incremental redundant index assignments. The incremental redundancy for HARQ is supplied by the source encoder and not the channel encoder. Simulation results show an excellent performance over a wide range of channel conditions, with inherently adapted bandwidth and complexity.