For practical communications which transmit finite blocks of source data over noisy channels, we question the common practice to compress (C) the source and then to add redundancy for error control. Rather we exploit the redundancy of the non-compressed source (NC) at the channel decoder by source-controlled channel-decoding. For a simple binary Markov source and a Rayleigh fading channel we simulated in a fair comparison the 2 systems (C and NC) using an ARQ/FEC scheme with rate-compatible punctured convolutional (RCPC) codes, Lempel-Ziv compression and a modified Viterbi decoder. We indicate parameter regions where it is better not to compress.