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 Plutos 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 light-curves. Results: We show that (i) Plutos surface pressure is currently in the 6.5-24 microbar range (ii) the methane mixing ratio is 0.5+/-0.1 %, adequate to explain Plutos inverted thermal structure and ~100 K upper atmosphere temperature (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 abundance of methane are strikingly similar, a possible consequence of the presence of a CH4-rich top surface layer.