Due to its low gain, the Orsay storage ring free-electron laser necessitates the use of high reflectivity mirrors. Three techniques for measuring the mirror losses are presented, based on cavity decay time measurements using either an external laser, the synchrotron radiation stored in the cavity, or the free-electron laser itself. The high signal-to-noise ratio allowed the detection of loss variations as low as 10(-7)/sec(1/2). From these diagnostics three distinct processes of UV-induced degradation of TiO2/SiO2 dielectric mirrors were identified. One was a surface absorption of the upper SiO2-air interface; it was not affected by annealing. The other two corresponded to a volume absorption of the layers which completely recovered after annealing.