The results show that air-sea coupling generally has a very small effect on daily-to-subseasonal tropical atmospheric predictability ranging from Kelvin waves to the MJO. It has much larger effects on longer-term variability, in both the atmosphere and ocean, including greatly increasing the amplitude of ENSO and lengthening its dominant period from two to four years. Consistent with these results, the eigenvectors of the system's dynamical evolution operator also separate into two distinct, but nonorthogonal, subspaces: one governing the nearly uncoupled daily-to-subseasonal dynamics, and the other governing the strongly coupled longer term dynamics. These subspaces arise naturally from the LIM analysis; no bandpass frequency filtering is applied. One implication of this remarkably clean separation of the uncoupled and coupled dynamics is that GCM errors in anomalous tropical air-sea coupling may cause substantial errors on interannual and longer time scales, but probably not on much shorter time scales such as those associated with the MJO. The moisture coupling is not so cleanly separated into different spaces, but its effects are clearly demonstrated by comparing the eigenmodes of two dynamical systems: the original LIM and a second system in which coupling of all other atmospheric variables to specific humidity anomalies is removed. Finally, the most predictable tropical states are determined, both for the full LIM and the uncoupled LIMs, and compared to the realized forecast skill.