The frequency noise of a single-frequency AlGaAs diode laser has been reduced by three orders of magnitude in the 0-400 kHz Fourier frequency range using a Fabry-Perot stabilisation scheme. A strong reduction of the 20 MHz free-running laser linewidth is observed when the fast servo loop is closed. Such laser diode spectral purity improvements are of great interest for optically pumped caesium beam atomic clocks, high resolution spectroscopy, heterodyne communications and fibre-optic sensors.