We study the eAects of a transverse magnetic field on the dynamics of the randomly diluted, dipolar coupled, Ising magnet LiHoo. ]()7Yog33F4. The transve'rse field mixes the eigenfunctions of the groundstate Ising doublet with the otherwise inaccessible excited-state levels. We observe a rapid decrease in the characteristic relaxation times, large changes in the spectral form of the relaxation,...