We theoretically study the influence of a predominant field-like spin-orbit torque on the magnetization switching of small devices with a uniform magnetization. We show that for a certain range of ratios (0.23-0.55) of the Slonczewski to the field-like torques, it is possible to deterministically switch the magnetization without requiring any external assist field. A precise control of the pulse length is not necessary, but the pulse edge sharpness is critical. The proposed switching scheme is numerically verified to be effective in devices by micromagnetic simulations. Switching without any external assist field is of great interest for the application of spin-orbit torques to magnetic memories.