PURPOSE: We propose a constrained optimization approach for designing parallel transmit (pTx) pulses satisfying all regulatory and hardware limits. We study the trade-offs between excitation accuracy, local and global specific absorption rate (SAR), and maximum and average power for small flip-angle pTx (eight channels) spokes pulses in the torso at 3 T and in the head at 7 T. METHODS: We compare the trade-offs between the above-mentioned quantities using the L-curve method. We use a primal-dual algorithm and a compressed set of local SAR matrices to design radio-frequency (RF) pulses satisfying all regulatory (including local SAR) and hardware constraints. RESULTS: Local SAR can be substantially reduced (factor of 2 or more) by explicitly constraining it in the pulse design process compared to constraining global SAR or pulse power alone. This often comes at the price of increased pulse power. CONCLUSION: Simultaneous control of power and SAR is needed for the design of pTx pulses that are safe and can be played on the scanner. Constraining a single quantity can create large increase in the others, which can then rise above safety or hardware limits. Simultaneous constraint of local SAR and power is fast enough to be applicable in a clinical setting. Magn Reson Med, 2013. (c) 2013 Wiley Periodicals, Inc.