We show that the divergence and moisture fields are exactly out of phase only when the system is at the SQE limit. A relaxation timescale dependent equivalent depth and “gross moist stability” are derived for both one-dimensional gravity waves and Kelvin waves. We show that rotation constrains moist Kelvin waves to be unconditionally stable at the SQE limit in our system. The wavenumber dependence of the effect of moisture is also analyzed, and it is seen that for any given value of the convective relaxation time, the larger scale waves are always closer to SQE than the smaller scale waves, as a natural consequence of the equivalence between SQE and the moisture-divergence phasing. The phasing between the height, divergence and moisture fields is calculated, and the behavior of moist gravity and Kelvin waves for finite relaxation timescales is explained using the phase differences between the various fields. Using this analysis, physically based explanations are provided for the results of prior GCM-based studies.