A powerful method to quantitatively control and direct exploration that combines the uncertainty (or variance) of three dimensional (3D) site characteristics with sensitivity of the performance model through a Taylor series expansion is demonstrated. Fundamentally, the approach is made possible by directly differentiating the performance model to obtain its 3D sensitivity to changes in subsurface properties. A one-time only direct differentiation of a generic code for performance analysis allows sensitivity to be determined with a single model run for any subsurface geometry. Thus direct differentiation avoids 1000's of model runs necessary with parameter perturbation or Monte Carlo simulation. The integrated exploration approach will be demonstrated with three examples, each with very different performance objectives (settlement, groundwater flow, and contaminant transport). The examples will demonstrate the process of producing calculated performance variance from 3D model sensitivity and uncertainty associated with site layer geometry and properties. Exploration is directed to locations of maximum variance in project performance. Sampling at these points produces the maximum reduction in performance uncertainty. As directed exploration proceeds, sufficiency of characterization effort is quantitatively determined through a reliability index. This index combines calculated performance, variance in calculated performance, and required performance.