The testing of optimization algorithms requires the running of problems with ill-conditioned Hessians. For constrained problems, it is the projection of the Hessian onto the space determined by the active constraints that must be ill conditioned. In this note it is argued that unless the Hessian and the constraints are constructed together, the constrained Hessian is likely to be well conditioned. The approach is to examine the effects of random constraints on a singular Hessian.