Native protein structures achieve stability in part by burying hydrophobic side-chains. About 75% of all amino acid residues buried in protein interiors are non-polar. Buried residues are not uniformly distributed in protein sequences, but sometimes cluster as contiguous polypeptide stretches that run through the interior of protein domain structures. Such regions have an intrinsically high local sequence density of non-polar residues, creating a potential problem: local non-polar sequences also promote protein misfolding and aggregation into non-native structures such as the amyloid fibrils in Alzheimer's disease. Here we show that long buried blocks of sequence in protein domains of known structure have, on average, a lower content of non-polar amino acids (about 70%) than do isolated buried residues (about 80%). This trend is observed both in small and in large protein domains and is independent of secondary structure. Long, completely non-polar buried stretches containing many large side-chains are particularly avoided. Aspartate residues that are incorporated in long buried stretches were found to make fewer polar interactions than those in short stretches, hinting that they may be destabilizing to the native state. We suggest that evolutionary pressure is acting on non-native properties, causing buried polar residues to be placed at positions where they would break up aggregation-prone non-polar sequences, perhaps even at some cost to native state stability.