We present results of on-sky tests performed in the summer of 2013 to characterize the performance of a prototype high-power pulsed laser for adaptive optics. The laser operates at a pulse repetition rate (PRR) of 600-800 Hz, with a 6% duty cycle. Its coupling e±ciency was found to be, in the best test case (using 18 W of transmitted power), 231 AE 14 photons s À1 sr À1 atom À1 W À1 m 2 when circular polarization was employed and 167 AE 17 photons s À1 sr À1 atom À1 W À1 m 2 with linear polarization. No improvement was seen when D 2b repumping was used, but this is likely due to the relatively large laser guide star (LGS) diameter, typically 10 arcsec or more, which resulted in low irradiance levels. Strong relaxation oscillations were present in the laser output, which have the e®ect of reducing the coupling e±ciency. To better understand the results, a physical modeling was performed using the measured pulse pro¯les and parameters speci¯c to these tests. The model results, for a 10 arcsec angular size LGS spot, agree well with the observations. When extrapolating the physical model for a sub-arcsecond angular size LGS (typical of what is needed for a successful astronomical guide star), the model predicts that this laser would have a coupling e±ciency of 130 photons s À1 sr À1 atom À1 W À1 m 2 , using circular polarization and D 2b repumping, for a LGS diameter of 0.6 arcsec Full Width at Half Maximum (FWHM), and free of relaxation oscillations in the 589 nm laser light.