We present tools for handling geometric constraint problems with under-constrained configurations. The basic idea is to add to the given set of constraints a set of extra constraints which can be defined either automatically or drawn from an independently given set of constraints placed on some geometric elements of the problem. In both cases, the resulting completed set of constraints is not over-constrained. If every well-constrained subproblem in the given under-constrained configuration is solvable, the completed constraint problem is also solvable.