We have analyzed all photometric observations of the 9 June 1988 occultation of the star P8 by Pluto in order to derive the radius of Pluto and certain parameters of its atmosphere. Our analysis is based on a "haze" model; but where relevant, we also discuss the thermal gradient model. With either model, the occultation observations yield a diameter for the limb of Pluto that is significantly larger than that found from mutual event observations by D. J. Tholen and M. W. Buie (1989, Bull. Am. Astron. Soc. 21, 981-982), but is in good agreement with the value from E. F. Young (1992, Ph.D. thesis, Massachusetts Institute of Technology). For a clear atmosphere (i.e., the thermal gradient model), we find the radius of the solid surface of Pluto and, obviously, also of the limb, to be 1195 ± 5 km. If the haze model is correct, the solid surface of the planet falls below 1180 ± 5 km, but the radius of the visible limb would be in the haze layer between 1185 and 1200 km. The degree to which the structure of Pluto's atmosphere is globally homogeneous is also discussed.