We present a graph drawing system for general undirected graphs with straight-line edges. It carries out a rather complex set of preprocessing steps, designed to produce a topologically good, but not necessarily nice-looking layout, which is then subjected to downhill-only version of Davidson and Harel's simulated annealing beautification algorithm. The intermediate layout is planar for planar graphs and attempts to come close to planar for non-planar graphs. The system's results are better and faster than what the annealing approach is able to achieve on its own.