An adaptive reduced-source approach is utilized for a Monte Carlo transport solution for the one-speed finite slab problem in [x,] geometry. Although a solution for the underlying problem has been available to arbitrary precision for some time, the purpose here is to demonstrate how the convergence afforded by traditional (nonadaptive) Monte Carlo can be improved significantly, without compromising its precision. It is demonstrated that the reduced-source Monte Carlo technique obtains multiple-orders-of-magnitude improvement over traditional Monte Carlo convergence for the two-dimensional transport problem treated. The goal is that ongoing research will obtain exponential convergence for practical applications that are not tractable with methodology currently available.