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To develop a new parallel transmit (pTx) pulse design for simultaneous multiband (MB) excitation in order to tackle simultaneously the problems of transmit B1 (B1+) inhomogeneity and total radiofrequency (RF) power, so as to allow for optimal RF excitation when using MB pulses for slice acceleration for high and ultrahigh field MRI.With the proposed approach, each of the bands that are simultaneously excited is subject to a band-specific set of B1 complex shim weights. The method was validated in the human brain at 7T using a 16-channel pTx system and was compared to conventional MB pulses operating in the circularly polarized (CP) mode. Further numerical simulations based on measured B1 maps were conducted.The new method improved B1+ homogeneity by 60% when keeping the total RF power constant and reduced total RF power by 72% when keeping the excitation fidelity constant, as compared to the conventional CP mode.A new pTx pulse design formalism is introduced targeting slice-specific B1+ homogenization in MB excitation while constraining total RF power. These pulses lead to significantly improved slice-wise B1+ uniformity and/or largely reduced total RF power, as compared to the conventionally employed MB pulses applied in the CP mode.