We present a high-performance Alexandrite laser for LIDAR applications with repetition rates up to 20 kHz in cavity-dumped Q-switched operation continuous-wave diode-pumped in the red spectral region. With a double-pass pump configuration, short pulses with 2.8 ns duration at repetition frequencies ranging from 1 kHz to 20 kHz could be demonstrated. At 5 kHz a – to our knowledge – record pulse energy of over 500 µJ could be achieved at 755 nm in TEM00. Furthermore, a stability measurement at an energy of around 350 µJ with 5 kHz showed no degradation over 150 Mega-shots. The influence of the crystal temperature on the laser performance is also investigated, first in continuous-wave and secondly in cavity-dumped Q-switched operation.