Projections of precipitation extremes in simulations with global climate models are very uncertain in the tropics, in part because of the use of parameterizations of deep convection. Here, we describe the behavior of precipitation extremes in high-resolution simulations that are run without a convective parameterization on a quasi-global aquaplanet. The frequency distributions of precipitation rates and precipitation cluster sizes in the tropics of a control simulation are similar to the observed distributions. In response to climate warming, three-hourly precipitation extremes increase at rates of up to 9%/K in the tropics because of a combination of positive thermodynamic and dynamic contributions. The dynamic contribution at different latitudes is connected to the vertical structure of warming using a moist static stability. If the precipitation rates are first averaged to a daily timescale and coarse-grained to a typical global climate-model resolution prior to calculating the precipitation extremes, the response of the precipitation extremes to warming becomes more similar to what was found previously in coarse-resolution aquaplanet studies. Importantly, the simulations studied here do not exhibit the high rates of increase of tropical precipitation extremes found in projections with some global climate models.