The experimental values of the (p, T) phase diagram of sulfur have been assessed through empirical equations commonly used. This treatment shows insufficiencies, namely those leading to significant uncertainties in the coordinates of the low-pressure triple points. An alternative way to try and find reliable equations for the phase equilibrium curves is provided by the exact integration of Clapeyron equation established and developed in a previous work. No fitting to (p, T) experimental data is then necessary. According to this method equations have been found to all the sulfur low-pressure equilibrium lines, and at the same time providing the enthalpies of transition between the phases as functions of temperature, and reliable values for the coordinates of the low-pressure triple points. The details of all these calculations and of the corresponding results are the object of the present paper. The (p, T) low-pressure phase diagram of sulfur is reconstructed on the basis of the results of the calculations carried out following these lines. (C) 2010 Elsevier Ltd. All rights reserved.