Variable-rate selective excitation (VERSE) is a radio frequency (RF) pulse reshaping technique. It is most commonly used to reduce the peak magnitude and specific absorption rate (SAR) of RF pulses by reshaping pulses and gradient waveforms to reduce RF magnitude while preserving excitation profiles. In this work, a general time-optimal VERSE algorithm for multidimensional and parallel transmit pulses is presented. Time optimality is achieved by translating peak RF limits to gradient upper bounds in excitation k -space. The limits are fed into a time-optimal gradient waveform design technique. Effective SAR reduction is achieved by reducing peak RF subject to a fixed pulse length. The presented method is different from other VERSE techniques in that it provides a noniterative time-optimal multidimensional solution, which drastically simplifies VERSE designs. Examples are given for 1D and 2D single channel and 2D parallel transmit pulses.Magn In magnetic resonance imaging (MRI), spatially selective excitation radio frequency (RF) pulses are often limited by hardware and pulse sequence constraints, such as RF power, peak RF magnitude, and SAR. In most imaging scenarios it is desirable to excite sharp slice profiles. However, such target profiles often result in oscillatory RF waveforms with high peak RF and unacceptable levels of SAR. High peak RF magnitude and SAR effectively set lower limits on the pulse length. In some fast imaging applications, the time required to perform excitation can reduce the available data acquisition time, resulting in SNR degradation (1). In other fast imaging applications, shorter TRs can be achieved by reducing SAR (2). Parallel transmission has recently gained the interest of researchers (3-9) because of the additional degrees of freedom afforded by excitation with multiple independent transmit coils. This can be used to shorten pulse duration, increase spatial resolution, and control RF power deposition (4). Numerical optimizationbased pulse design methods are widely used to design parallel transmit pulses (3-9). Numerical optimization is necessary to meet the unique requirements of parallel RF