Cloud-scale models apply two drastically different methods to represent condensation of water vapor to form and grow cloud droplets. Maintenance of water saturation inside liquid clouds is assumed in the computationally efficient saturation adjustment approach used in most bulk microphysics schemes. When super- or subsaturations are allowed, condensation/evaporation can be calculated using the predicted saturation ratio and (either predicted or prescribed) mean droplet radius and concentration. The study investigates differences between simulations of deep unorganized convection applying a saturation adjustment condensation scheme (SADJ) and a scheme with supersaturation prediction (SPRE). A double-moment microphysics scheme with CCN activation parameterized as a function of the local vertical velocity is applied to compare cloud fields simulated applying SPRE and SADJ. Clean CCN conditions are assumed to demonstrate upper limits of the SPRE and SADJ difference. Microphysical piggybacking is used to extract the impacts with confidence. Results show a significant impact on deep convection dynamics, with SADJ featuring more cloud buoyancy and thus stronger updrafts. This leads to around a 3% increase of the surface rain accumulation in SADJ. Upper-tropospheric anvil cloud fractions are much larger in SPRE than in SADJ because of the higher ice concentrations and thus longer residence times of anvil particles in SPRE, as demonstrated by sensitivity tests. Higher ice concentrations in SPRE come from significantly larger ice supersaturations in strong convective updrafts that feature water supersaturations of several percent.