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In this paper, we propose an iterative Kalman filtering scheme that has faster convergence and introduces less residual noise, when compared with the iterative scheme of Gibson, et al. This is achieved via the use of long and overlapped frames as well as using a tapered window with a large side lobe attenuation for linear prediction analysis. We show that the Dolph-Chebychev window with a -200 dB side lobe attenuation tends to enhance the dynamic range of the formant structure of speech corrupted with white noise, reduce prediction error variance bias, as well as provide for some spectral smoothing, while the long overlapped frames provide for reliable autocorrelation estimates and temporal smoothing. Speech enhancement experiments on the NOIZEUS corpus show that the proposed method outperformed conventional iterative and non-iterative Kalman filters as well as other enhancement methods such as MMSE-STSA and PSC.