The time evolution of spins-1/2 subject to radiation damping, which is commonly encountered for solvent peaks at high field, is examined in detail. The well-known analytic results for rectangular pulses on undamped spin-1/2 systems are extended to the radiation damped case, and reveal surprisingly complex dynamics. Explanations in terms of Bloch vectors are also presented, and composite pulse sequences which would also be insensitive to radiation damping are proposed. In addition, gradient optimization programs were developed to find shaped π and π/2 pulses insensitive to radiation damping. The optimized pulses compensate for radiation damping effects even when the characteristic damping time is shorter than the pulse length. © 1989 American Institute of Physics.