[en] Using an extended version of the optimal-control-based gradient ascent pulse engineering algorithm, cooperative (COOP) pulses are designed for multi-scan experiments to prepare pseudo-pure states in quantum computation. COOP pulses can cancel undesired signal contributions, complementing and generalizing phase cycles. They also provide more flexibility and, in particular, eliminate the need to select specific individual target states and achieve the fidelity of theoretical limit by flexibly choosing appropriate number of scans and duration of pulses. The COOP approach is experimentally demonstrated for three-qubit and four-qubit systems.