In this work we describe the increased efficiency obtained in solid-state coherence-transfer NMR experiments involving quadrupolar nuclei by carrying out cross-polarization while the sample is spinning along an axis parallel to the magnetic field. After the cross-polarization step, the spinning axis is rapidly switched to the "magic angle" for detection of a high-resolution free induction decay from the target nuclei. The increased efficiency of the cross-polarization process, coupled with the superior resolution available from magic-angle sample spinning, is useful for obtaining high-resolution NMR spectra of slowly-relaxing spin species in condensed phases. A specific example illustrating this method is drawn from the cross-polarization of magnetization from aluminum-27 spins to phosphorus-31 spins in the large-pore aluminophosphate VPI-5.