A diode-laser-pumped Nd:YAG laser is frequency stabilized by locking its frequency-doubled output to the center of unsaturated (Doppler-broadened) transitions of the (127)I(2) molecule. The successive two-sample deviation of the laser frequency (root Allan variance) is kept below 5.67 kHz, or 2 parts in 10(11) of the laser frequency, for averaging times between 10 ms and 40 s. This locking technique is simpler and requires less laser power than locking to Doppler-free lines.