The skewed Kalman filter (SKF) extends the classical Gaussian Kalman filter (KF) by accommodating asymmetric (skewed) error distributions in linear state-space models. We introduce a computationally efficient method to address the curse of increasing skewness dimensions inherent in the {SKF}. Building on insights into how skewness propagates through the state-space system, we derive an algorithm that discards elements in the cumulative distribution functions which do not affect asymmetry beyond a pre-specified numerical threshold; we refer to this approach as the pruned skewed Kalman filter (PSKF). Through extensive simulation studies on both univariate and multivariate state-space models, we demonstrate the proposed method’s accuracy and efficiency. Furthermore, we are first to derive the skewed Kalman smoother and implement its pruned variant. We illustrate its practical relevance by estimating a linearized New Keynesian DSGE model with U.S. data under both maximum likelihood and Bayesian MCMC frameworks. The results reveal a strong preference for skewed error distributions, especially in productivity and monetary policy shocks.