  We study the thermodynamic behavior of the random chain model proposed by
Iori, Marinari and Parisi, and how this depends on the actual sequence of
interactions along the chain. The properties of randomly chosen sequences are
compared to those of designed ones, obtained through a simulated annealing
procedure in sequence space. We show that the transition to the folded phase
takes place at a smaller strength of the quenched disorder for designed
sequences. As a result, folding can be relatively fast for these sequences.
