The interface motion for Cu electrodeposition in additive-free and thiourea-containing acid plating baths using three-dimensional and quasi-two-dimensional electrochemical cells was followed in real time in the potential range where the kinetics of the reaction is dominated by activation and Ohmic overpotentials. In the additive-free plating bath the growing interface changes from a marginally stable (nodular) to an unstable (branched) regime as the activation overpotential/Ohmic overpotential ratio decreases. The presence of thiourea drives the interface motion to a steady-state regime in which the predictions of the Edwards−Wilkinson equation for the interface motion are obeyed. The influence of thiourea on Cu electrodeposition is to slow the growth rate at protrusions and to increase the growth rate at flat surface domains or valleys, leading to a smoothing of the entire growing electrodeposit surface.