Many data compression methods cannot remove all redundancy from a file that they compress because it can be encoded to many compressed files. In particular, we consider the redundancy caused by the availability of many equivalent messages. A canonical example is that of the many longest matches that are typically found by the LZ77 derivatives. Most of this redundancy can be removed using a technique previously introduced by the authors as bit recycling. Until now, bit recycling has been applied to LZ77 derivatives. In this paper, we consider a more general case: the one when there are multiple equivalent messages available to the compressor. We extend an algorithm, called resolution, that allows to include bit recycling in a compressor that proceeds in a stream-like fashion. Finally, we study the efficiency of proportional recycling.