  Finding control fields (pulse sequences) that can compensate for the
dispersion in the parameters governing the evolution of a quantum system is an
important problem in coherent spectroscopy and quantum information processing.
The use of composite pulses for compensating dispersion in system dynamics is
widely known and applied. In this paper, we make explicit the key aspects of
the dynamics that makes such a compensation possible. We highlight the role of
Lie algebras and non-commutativity in the design of a compensating pulse
sequence. Finally we investigate three common dispersions in NMR spectroscopy,
the Larmor dispersion, rf-inhomogeneity and strength of couplings between the
spins.
