In this note we offer a reply to Idsardi (2006b) responding to Kornai (2006),
 where we questioned the strength of the demonstration offered in Idsardi
 (2006a) that the decision problem whether a particular string is licensed by
 an OT grammar is NP-hard. We present a simple bound, min(n,p,2^c) for the 
 maximum Hamilton search problem that could be encoded in the grammar, where 
 n is the size of the domain, p is the size of the inventory, and c is the 
 number of constraints operating in parallel, and argue that OT is guarded from
 computational blow-up by the fact that this number is small.