We have derived a novel method to assess compositional biases in biological sequences, which is based on finding the lowest-probability subsequences for a given residue-type set. As a case study, the distribution of prion-like glutamine/asparagine-rich ((Q+N)-rich) domains (which are linked to amyloidogenesis) was assessed for budding and fission yeasts and four other eukaryotes. We find more than 170 prion-like (Q+N)-rich regions in budding yeast, and, strikingly, many fewer in fission yeast. Also, some residues, such as tryptophan or isoleucine, are unlikely to form biased regions in any eukaryotic proteome.