Analytical and numerical solutions are employed to examine the concentration history of a dissolved substance in water pumped from a leaky aquifer. Many aquifer systems are characterized by stratification, for example, a sandy layer overlain by a clay layer. To obtain information about separate hydrogeologic units, aquifer pumping tests are often conducted with a well penetrating only one of the layers. When the initial concentration distribution is also stratified (the concentration varies with elevation only), the concentration breakthrough in the pumped well may be interpreted to provide information on aquifer hydraulic and transport properties. To facilitate this interpretation, we present some simple analytical and numerical solutions for limiting cases and illustrate their application to a fractured bedrock/glacial drift aquifer system where the solute of interest is dissolved radon gas. In addition to qualitative information on water source, this method may yield estimates of effective porosity and saturated thickness (or fracture transport aperture) from a single-hole test. Little information about dispersivity is obtained because the measured concentration is not significantly affected by dispersion in the aquifer.