A new importance map approach for Monte Carlo simulation that can be used in an adaptive fashion has been identified and developed. It is based on using a mesh-based system of weight windows that are independent of any physical geometric cells. It consists of an importance map generator and a splitting and Russian roulette algorithm for a mesh-based weight windows game that is used in an iterative fashion to obtain increasingly efficient results. The general purpose Monte Carlo code MCNP is modified to incorporate this new mesh-based importance map generator and matching weight window technique for variance reduction. Two nuclear well logging problems—one for neutrons and the other for gamma rays—are used to test the new importance map generator. Results show that the new generator is able to produce four to six times larger figures of merit than MCNP’s physical geometry cell-based importance map generator. More importantly, the superior user friendliness of this new mesh-based generator makes variance reduction easy to accomplish.