Abstract: The tandem algorithm combines the marching cube algorithm for surface extraction and the edge contraction algorithm for surface simplification in lock-step to avoid the costly intermediate step of storing the entire extracted surface triangulation. Beyond this basic strategy, we introduce refinements to prevent artifacts in the resulting triangulation, first, by carefully monitoring the amount of simplification during the process and, second, by driving the simplification toward a compromise between shape approximation and mesh quality. We have implemented the algorithm and used extensive computational experiments to document the effects of various design options and to further fine-tune the algorithm.