Proteins often contain regions that are compositionally biased (CB), i.e., they are made from a small subset of amino-acid residue types. These CB regions can be functionally important, e.g., the prion-forming and prion-like regions that are rich in asparagine and glutamine residues. Here I report a new program fLPS that can rapidly annotate CB regions. It discovers both single-residue and multiple-residue biases. It works through a process of probability minimization. First, contigs are constructed for each amino-acid type out of sequence windows with a low degree of bias; second, these contigs are searched exhaustively for low-probability subsequences (LPSs); third, such LPSs are iteratively assessed for merger into possible multiple-residue biases. At each of these stages, efficiency measures are taken to avoid or delay probability calculations unless/until they are necessary. On a current desktop workstation, the fLPS algorithm can annotate the biased regions of the yeast proteome (>5,700 sequences) in 65 million sequences) in as little as ~1 hour. fLPS discovers both shorter CB regions (of the sort that are often termed 'low-complexity sequence'), and milder biases that may only be detectable over long tracts of sequence. fLPS can readily handle very large protein data sets, such as might come from metagenomics projects. It is useful in searching for proteins with similar CB regions, and for making functional inferences about CB regions for a protein of interest.