The N-14 nuclear magnetic resonance spectra of polycrystalline samples of KNO3, NH4NO3, and several amino acids have been studied under the condition of magic angle spinning. These compounds have N-14 quadrupolar coupling constants of about 1 MHz, but it is possible to obtain peaks with linewidths of a few hundred Hz and good signal/noise ratio. The spectra contain information on both isotropic chemical shifts and quadrupolar coupling constants. The effect of very small deviations from the magic angle (less than or equal to 0.05 degrees) is studied, and the corresponding spectral features are analyzed qualitatively and quantitatively. The use of a weak pulse or a weak composite pulse causes an increase in the signal intensity, and an analysis is given to explain these unusual results.