We describe a novel fast straightforward folding algorithm for HP (hydrophobic- polar) t,ype lattice proteins. It, is de-signed after the concept of unguided, cotranslational folding of a nascent. peptide. It is tlcterminist~ic and runs in O ( 17) in the chain length. Acrur-acy of prediction is governed by t,hr searc11 tlcl)th of t,llc, algorithtn that is “looked ahead ” at each chain growth st el’. I,ong range interactions are significantly incrcas<~tl and c’rlergy barriers become less prohibitive with increasing search depth. ‘I’tle csfficiency of sequential fold-ing is test & arid rc:sults comparetl to related methods. All characterist its of the HP-motlcl buch as formation of a hy-drophobic core and overall compact structures are observed. Sinccl the procrt1ln.c is very fast and flexible we obtain a use-ful tool to approxirnatt ~ t.he sqric-nce t.0 st,ructlire mapping of t)iopotymers in general antI to study the complex interplay of folding strat,rgies, pot,entials and alphabets with large en-sembles of random structures.