Climate models often project an increase of rainfall under global warming over the climatologic wet regions from the global zonal-mean perspective. However, this “rich-get-richer” mechanism is not valid on a basin scale. In this study by analyzing climate change experiment outputs from an idealized atmospheric general circulation model with uniform sea surface warming and the Coupled Model Intercomparison Project Phase 5 (CMIP5) models, we note that the intertropical convergence zones along the equatorial Indian Ocean and the equatorial Atlantic Ocean exhibit a very different response to anthropogenic forcing. In the present-day climate in boreal summer (winter), the tropical Indian (Atlantic) Ocean exhibits two pronounced rainbands, with one branch located over the Indian monsoon (Amazon) region and the other located near the equator. In future warmer climate, the two rainbands compete through a local Hadley circulation; as a result, only the stronger branch becomes wetter while the weaker one affected by anomalous descending motion and moisture divergence becomes drier. Thus, on a basin scale, the wet does not always get wetter.