  We demonstrate a technique to measure hyperfine structure using a
frequency-stabilized diode laser and an acousto-optic modulator locked to the
frequency difference between two hyperfine peaks. We use this technique to
measure hyperfine intervals in the $5P_{3/2}$ state of $^{85}$Rb and obtain a
precision of 20 kHz. We extract values for the magnetic-dipole coupling
constant $A=25.038(5)$ MHz and the electric-quadrupole coupling constant
$B=26.011(22)$ MHz. These values are a significant improvement over previous
results.
