A tropical ocean-atmosphere model of intermediate complexity, incorporating a limited set of physical processes, is used to investigate variability up to interannual timescales. The model atmosphere has a single vertical mode and an explicit moisture budget, whereas the ocean has one active upper layer. Basic experiments confined to a Pacific-size closed ocean basin and the overlying atmosphere are described. Eastward-propagating coupled waves with a period of about six years arise for strong coupling, but with weak coupling a steady equilibrium is reached. The model has no internal high-frequency variability, so for some cases a small amount of noise is added to the atmospheric forcing terms. This noise is selectively amplified by moist processes in the atmosphere to generate eastward-propagating intraseasonal waves. It is found that these waves have little effect on the robust interannual coupled wave: rather, the interannual mode imposes large-scale patterns that inhibit the intraseasonal waves.