  Pressure-induced variations of $^{27}$Al NMR spectra of CeAl$_3$ indicate
significant changes in the ground-state characteristics of this prototypical
heavy-electron compound. Previously reported magnetic and electronic
inhomogeneities at ambient pressure and very low temperatures are removed with
external pressures exceeding 1.2 kbar. The spectra and results of corresponding
measurements of the NMR spin-lattice relaxation rates indicate a
pressure-induced emergence of a simple paramagnetic state involving electrons
with moderately enhanced masses and no magnetic order above 65 mK.
