When the short-time Fourier transform (STFT) of an audio signal is arbitrarily modified, it no longer truly represents a time-domain signal. Classically, the accepted solution to obtain a time-domain signal from a modified STFT (MSTFT) is to invert the MSTFT to a time-domain signal that has an STFT that is closest to the MSTFT in a least squares sense. This is also the approach currently taken by our modulation filtering techniques. However, it was never established that using the original and unmodified STFT phase in this reconstruction is optimal for modulation filtering. In this paper, we compare our signal reconstruction approach to a well-known iterative procedure that approximates a time-domain signal using only the STFT magnitude. We analyze the signal reconstruction of speech signals after filtering them with low-pass, band-pass and high-pass modulation filters. Our study shows that the iterative procedure yields quantitatively and qualitatively comparable signals at significantly higher computational cost. It therefore does not seem a worthwhile alternative to our current reconstruction technique, but it may prove useful for IIR modulation filtering.