We have investigated the morphological instabilities in electrochemical compact growth. The experimental system consisted in 0.5 M aqueous solutions of CuSO4 in a quasi-2D strip geometry. The deposits were made at low constant current densities ranging between 20 and 100 mA cm−2. We monitored the morphology of the growing interface and the electrical parameters of the system. We find two different growth regimes: at short times the interfaces show roughness scaling with a roughness exponent, α = 0.78 ± 0.05; at longer times an instability develops which causes an increase in the growth speed and the external applied voltage. Some characteristic time and length scales of this latter instability compare well with theoretical results in directional solidification models.