We demonstrate the coherent optical control of magnetization precession in a thin Ni film by a second excitation pulse, which amplifies or attenuates the precession induced by a first pulse depending on the fluences of the pump-pulses and the pump-pump delay. This control goes beyond the conventional strategy, where the same mechanism drives the precession in-phase or out-of-phase. We balance the magneto-acoustic mechanism driven by quasi-static strain and the shape-anisotropy change triggered by laser-induced demagnetization. These mechanisms tilt the transient effective magnetic field in opposite directions in the case of negative magneto-elastic coupling (b1<0). While the strain response is linear in the fluence, demagnetization is nonlinear near the Curie temperature, enabling fluence-based control scenarios.