Context. Pluto possesses a thin atmosphere, primarily composed of nitrogen, in which the detection of methane has been reported. Aims. The goal is to constrain essential but so far unknown parameters of Pluto's atmosphere, such as the surface pressure, lower atmosphere thermal stucture, and methane mixing ratio. Methods. We use high-resolution spectroscopic observations of gaseous methane and a novel analysis of occultation lightcurves. Results. We show that (i) Pluto's surface pressure is currently in the 6.5-24 μbar range, (ii) the methane mixing ratio is 0.5 ± 0.1%, adequate to explain Pluto's inverted thermal structure and ∼100 K upper atmosphere temperature, and (iii) a troposphere is not required by our data, but if present, it has a depth of at most 17 km, i.e. less than one pressure scale height; in this case methane is supersaturated in most of it. The atmospheric and bulk surface abundances of methane are strikingly similar, a possible consequence of a CH 4 -rich top surface layer.