Carr-Purcell-Meiboom-Gill (CPMG) relaxation measurements employing trains of 180degrees pulses with variable pulse spacing provide valuable information about systems undergoing millisecond-time-scale chemical exchange. Fits of the CPMG relaxation dispersion profiles yield rates of interconversion, relative populations, and absolute values of chemical shift differences between the exchanging states, \Deltaomega\. It is shown that the sign of Deltaomega that is lacking from CPMG dispersion experiments can be obtained from a comparison of chemical shifts in the indirect dimensions in either a pair of HSQC (heteronuclear single quantum coherence) spectra recorded at different magnetic fields or HSQC and HMQC (heteronuclear multiple quantum coherence) spectra obtained at a single field. The methodology is illustrated with an application to a cavity mutant of T4 lysozyme in which a leucine at position 99 has been replaced by an alanine, giving rise to exchange between ground state and excited state conformations with a rate on the order of 1450 s(-1) at 25 degreesC.