Despite the fact that many publications have dealt with asphaltene onset pressure (AOP) lines during the last 2 or 3 decades, no explicit method for tracing these and other related boundaries from equation of state (EoS) models has been proposed in the literature. In this work, a new integral algorithmic strategy for the construction of complete phase envelope diagrams based on an EoS is presented. The method of Michelsen for tracing two-phase boundaries is used, while for three-phase saturation lines, an equivalent method was designed, including a second set of K factors and a phase fraction as extra independent variables. The double-saturation point is defined, and its importance is highlighted, from both phase behavior and algorithmic perspectives. Specific issues as recognition of unstable segments, such as false bubble curves, are also discussed. Three different fluids from the literature are taken as case studies to illustrate the application of the proposed strategy and discuss different types of behavior. In particular, an unexpected second three-phase region was predicted at higher temperatures in two of the three cases studied. This could serve as inspiration for new experimental studies, to see whether the existence of such a region can be confirmed for some reservoir fluids, or it could be just an artificial behavior predicted by the models. In summary, computer codes based on the proposed strategy might become a useful tool for researchers or professionals dealing with asphaltene phase behavior in reservoir fluids.