A detailed analysis is presented of a method to eliminate transverse magnetization prior to each rf excitation in pulse sequences with TR less than T2. It is shown that artifact-free images with high T1 contrast can be obtained only if a phase shift that is incremented during each TR interval is applied to the transverse magnetization. Computer simulations are used to show that when this phase increment is 117 degrees, the steady-state transverse magnetization prior to each rf pulse is nulled over a wide range of T1, T2, and rf tip angles, resulting in optimal T1 contrast. Such nulling of steady-state transverse magnetization cannot be obtained by using large gradient pulses, or gradients of random or linearly incremented amplitude. Images of phantoms and human subjects confirm the theoretical predictions.