We consider the problems of finding the lexicographically
minimal (or maximal) satisfying assignment of propositional
formulae for different restricted formula classes. It turns
out that for each class from our framework, the above problem
is either polynomial time solvable or complete for OptP. We
also consider the problem of deciding if in the optimal
assignment the largest variable gets value 1. We show that
this problem is either in P or P^NP complete.