This paper presents two ways to improve the Real-Time Iterative Spectrogram Inversion (RTISI) algorithm. The standard RTISI phase estimator with look-ahead processes the buffered frames in reverse order. We show that better results are achieved by controlling this order according to frame energy. Another improvement is to initialize the last row of the phase estimator buffer by progressing the unwrapped phase difference of the previous frames. Furthermore, we extend these improvements to dual window length phase estimation and analyze the performance in SER with respect to different analysis window lengths.