This papers describes an estimator for a standard state-space model with coefficients generated by a random walk that is statistically superior to the Kalman filter as applied to this particular class of models. Two closely related estimators for the variances are introduced: A maximum likelihood estimator and a moments estimator that builds on the idea that some moments are equalized to their expectations. These estimators perform quite similar in many cases. In some cases, however, the moments estimator is preferable both to the proposed likelihood estimator and the Kalman filter, as implemented in the program package Eviews.