Maximum entropy problems and other models having a large number of superbasic variables can be costly to solve with methods using dense reduced Hessian approximations. In many cases, such problems can be solved effectively by using exact Hessians in conjunction with optimization methods capable of utilizing them. For example, PATHNLP uses second-order information to reformulate the original optimization problem as a complementarity problem. We discuss the advantages and drawbacks of this approach and the recently-introduced capability to compute second-order information in a GAMS environment. Computational results from several maximum entropy problems (or similar) using PATHNLP are reported.