Shaped radiofrequency pulses are designed to extend the quadrupole-echo excitation bandwidth without insidious phase distortions. The quadrupole-shaped pulse (QUASH) is constructed by a simple iterative optimization procedure which directly solves a density-matrix equation of motion for an arbitrary amplitude-modulated pulse acting on a three-level system. Computer simulations and experimental 2H NMR studies comparing the performance of simple rectangular, composite, and shaped quadrupole-echo sequences on the partially rotating methyl group on 1-alanine-d3,3,3 show a dramatic improvement using the shaped excitation pulse. Increases in the effective bandwidth by a factor of two and three were realized over composite and rectangular sequences, respectively, without phase distortions. © 1992.