The results show that air-sea coupling generally has a very small effect on daily-to-subseasonal tropical atmospheric variability 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.