This study uses large-eddy simulations to investigate processes of moist convection initiation (CI) over heterogeneous surface fluxes. Surface energy balance is imposed via a 1808 phase lag of the surface moisture flux (relative to the sensible heat flux), such that the relatively warm surface is relatively dry (and the relatively cool surface is relatively wet). As shown in previous simulations, a mesoscale circulation forms in the presence of surface-flux heterogeneity, which coexists with turbulent fluctuations. The mesoscale convergence zone of this circulation develops over the relatively warm surface, and this is where clouds first form. Convection initiation occurs sooner as the amplitude of the heterogeneity increases, and as the surface moisture increases (i.e., Bowen ratio decreases). Shallow clouds initiate when boundary layer heights (z i ) become greater than the lifting condensation level (LCL). Deep precipitating clouds initiate when the LCL and level of free convection (LFC) are roughly the same when averaged over the relatively warm surface, which is equivalent to the mean convective inhibition (CIN) becoming nearly zero. From the perspective of the entire (mesoscale) domain, cases with strongly heterogeneous surfaces have a wider distribution of both z i and LCL. Thus, a comparison of z i with LCL over a mesoscale area (i.e., within one mesoscale model grid box) may lead to misleading conclusions about CI and cloud-base height. It is also shown that as the amplitude of the surfaceflux heterogeneity increases the mesoscale convergence zone becomes narrower and stronger. Furthermore, CI occurs earlier over relatively wet surfaces partly because turbulent eddies are more vigorous owing to slightly greater buoyancy.