Reducing the model spread in free-tropospheric relative humidity (RH) and its response to warming is a crucial step towards reducing the uncertainty in clear-sky climate sensitivity, a step that is hoped to be taken with recently developed global storm-resolving models (GSRMs). In this study we quantify the inter-model differences in tropical present-day RH across GSRMs, making use of DYAMOND, a first 40-day intercomparison. We find that the inter-model spread in tropical mean free-tropospheric RH is reduced compared to conventional atmospheric models, except from the the tropopause region and the transition to the boundary layer. We estimate the reduction to approximately 50-70% in the upper troposphere and 25-50% in the mid troposphere. However, the remaining RH differences still result in a spread of 1.2 Wm-2 in tropical mean clear-sky outgoing longwave radiation (OLR). This spread is mainly caused by RH differences in the lower and mid free troposphere, whereas RH differences in the upper troposphere have a minor impact. By examining model differences in moisture space we identify two regimes with a particularly large contribution to the spread in tropical mean clear-sky OLR: rather moist regimes at the transition from deep convective to subsidence regimes and very dry subsidence regimes. Particularly for these regimes a better understanding of the processes controlling the RH biases is needed.