The Area method, developed recently for solving multicomponent phase equilibrium problems, has been extended to pure fluids. The method is based on maximizing a single objective function in the Helmholtz-volume surface along any given isotherm, which reduces the number of independent variables to only two : the saturated liquid and vapour volumes. Two techniques are employed to find the maximum of the objective function, the integral and iterative. The integral always finds the thermodynamically stable solution without any prior assumptions about the values of the molar volumes. This factor distinguishes the integral from the iterative technique and also from methods based on the Maxwell equal-area principle. The method has been applied to a group of high accuracy non-cubic equations of state and some of the thermodynamic inconsistencies which occur inside the two-phase region are explored. A new inequality constraint which eliminates these inconsistencies during the development of new equations of state is proposed, and initial results with fitting a preliminary Helmholtz equation of state for benzene are encouraging.