Introduction Parallel RF transmit (Tx) offers additional degrees of freedom (redundancy) in excitation pulse design [1,2]. One application of this redundancy is accelerating multidimensional selective excitation by under-sampling the excitation k space. Unlike the spatial encoding task in imaging, where the underlying image is unknown, in the case of excitation pulse design the target excitation profile is known a priori. This provides a Bloch equation-based RF pulse design with great opportunities for optimization. In principle, the target profile, B1 maps and error tolerance (TOL) determine where to ideally under-sample the k space with optimal sparsity. It is desirable to have a sparsifying strategy that exploits this pre-knowledge [3,4]. We propose a k-space sparsifying method based on a greedy-wise algorithm. Our approach is inspired by the theoretical results in sparse signal approximation [5,6,7] and the Compressed Sensing (CS) effort on the imaging side [8,9]. In the sense of ‘sparsity’ our approach can be seen as a counterpart to the multi-coil CS in RF excitation. Simulation and phantom results showed good excitation profile particularly in high reduction-factor cases, where the conventional non-adaptive under-sampling method is limited.