Many current uses of fluid phase equilibria would benefit from new equations of state that are more accurate in fitting experimental data and more certain of their predictions for unmeasured phase equilibria. We present a first step towards a fitting procedure which incorporates the advantages of critical scaling theory in the vicinity of the critical point with the advantages of ’classical’ cubic equations of state far from the critical point. For VLE, we propose a non-linear order parameter (density variable) that captures the familiar fluid asymmetry in the far from critical vapor and liquid regimes without affecting the linear density-dependence in the near critical regime; this complements earlier work for LLE. Use of this order parameter in describing the liquid-vapor phase boundary effects a ’heuristic’ crossover from accurate critical point behavior to accurate far-from-critical behavior. The accuracy of this procedure has been verified by using it to fit data from the open literature for the vapor-liquid phase boundary for a variety of one component systems : with polar molecules (chlorotrifluoromethane), with small non-polar molecules (carbon dioxide, ethane), and with the heavier normal alkanes (pentane, hexane, heptane, octane, and nonane). Within 100 k of the critical point, this method is substantially more accurate than its competitors. At worst, in the far-from-critical (e.g. 200-300 K below the critical point) regime, this procedure seems to consistently overestimate the vapor densities by a small amount (less than 3%).