The incorporation of prior information, including personal knowledge about the smoothness and correlation length for the permeability field, is essential to reservoir characterization from well test data if highly heterogeneous models are needed for simulation of multiphase flow in the interwell region. The same assumptions about continuity and smoothness that stabilize the kriging estimate and allow the calculation of conditional realizations of permeability fields from sparse data can be used to stabilize the nonlinear incorporation of transient pressure data. In this paper I outline an approach for generating, from well test data and prior information, a reservoir model with the following properties: (1) Previous measurements of reservoir parameters are honored. (2) Previous well tests are honored. (3) It is a smoothed version of the true distribution. (4) Additional information can be incorporated when it becomes available. Conditional realizations of the permeability and porosity fields are generated using Cholesky decomposition of the model covariance matrix. The method proved to be stable and efficient when it was applied to two synthetic reservoir models with up to 1,089 unknown parameters.