Combining the model of unguided, cotranslational folding of a nascent peptide chain with HP lattice proteins we designed a fast and straightforward folding algorithm. In choosing the search depth that is “looked ahead” at each chain growth step we tradeoff conformational search and accuracy against computational demands. We test the performance by folding short sequences with known, unique ground states. We find a success-rate, large enough to consider cotranslational foldability as a potential evolutionary fitness criterion. Characterizing the sequence to structure relation we find analogies to ground state ensembles: structure fitness landscapes are very rugged and there are few frequent and many rare structures. We conclude that our simple folding model is well suited for a realistic approximation of ensemble properties that we consider as crucial to understand the evolutionary dynamics of biopolymers.