Spatially tailored radio frequency (RF) excitations accelerated with parallel transmit systems provide the opportunity to create shaped volume excitations or mitigate inhomogeneous B(1) excitation profiles with clinically relevant pulse lengths. While such excitations are often designed as a least-squares optimized approximation to a target magnitude and phase profile, adherence to the target phase profile is usually not important as long as the excitation phase is slowly varying compared with the voxel dimension. In this work, we demonstrate a method for a magnitude least squares optimization of the target magnetization profile for multichannel parallel excitation to improve the magnitude profile and reduce the RF power at the cost of a less uniform phase profile. The method enables the designer to trade off the allowed spatial phase variation for the improvement in magnitude profile and reduction in RF power. We validate the method with simulation studies and demonstrate its performance in fourfold accelerated two-dimensional spiral excitations, as well as for uniform in-plane slice selective parallel excitations using an eight-channel transmit array on a 7T human MRI scanner. The experimental results are in good agreement with the simulations, which show significant improvement in the magnitude profile and reductions in the required RF power while still maintaining negligible intravoxel phase variation.