Motivated by our own industrial users, we attack the following challenge that is crucial in many practical planning, scheduling or timetabling applications. Assume that a solver has found a solution for a given hard problem and, due to unforeseen circumstances (e.g., re-scheduling), or after an analysis by a committee, a few more constraints have to be added and the solver has to be re-run. Then it is almost always important that the new solution is "close" to the original one. The activity-based variable selection heuristics used by SAT solvers make search chaotic, i.e., extremely sensitive to the initial conditions. Therefore, re-running with just one additional clause added at the end of the input usually gives a completely different solution. We show that naive approaches for finding close solutions do not work at all, and that solving the Boolean optimization problem is far too inefficient: to find a reasonably close solution, state-of-the-art tools typically require much more time than was needed to solve the original problem. Here we propose the first (to our knowledge) approach that obtains close solutions quickly. In fact, it typically finds the optimal (i.e., closest) solution in only 25% of the time the solver took in solving the original problem. Our approach requires no deep theoretical or conceptual innovations. Still, it is non-trivial to come up with and will certainly be valuable for researchers and practitioners facing the same problem.