A predictor–corrector approach for parameter estimation is discussed and improved upon. The predictor applies sequential parameter estimation to obtain an estimate with few degrees of freedom, using only part of the available information. A new termination criterion for sequential estimation is proposed to avoid over-parameterization and to terminate the predictor at a stage which is advantageous for the final estimate. The corrector downscales the predictor estimate in a two-step procedure involving all available information, including the estimate obtained with the predictor. The first corrector step is a variant of Kriging. The second corrector step is a parameter estimation, again involving few degrees of freedom, with basis functions derived from the results of the predictor. The methodology is applied to estimate the fluid conductivity in a porous medium. Numerical experiments demonstrate the usefulness of the predictor–corrector approach and show that the new termination criterion for the predictor is important to obtain a good final estimate.