The Kalman recursion is a powerful technique for reconstruction of the speech signal observed in additive background noise. In contrast to Wiener filtering and spectral subtraction schemes, the Kalman algorithm can be easily implemented in both causal and noncausal form. After studying the perceptual differences between these two implementations we propose a novel algorithm that combines the low complexity and the robustness of the Kalman filter and the proper noise shaping of the Kalman smoother.