A theory of optimum burst excitation is developed in the framework of the Shinnar-LeRoux spinor formalism. An N pulse RF train of constant or linear phase cannot improve on an average echo strength of M0/N, and a phase modulation of the pulse train is necessary to improve the signal yield to the theoretical maximum value M0 square root of N. Several methods are presented yielding pulse trains of nearly optimum average amplitude for arbitrary N. It is shown that RF phase spoiling can be analyzed with the same framework. The presented pulse trains may also be useful when ultrawide spectrum hard pulses are required, but only limited RF power is available, e.g., for NMR experiments in extremely inhomogeneous B0 fields.