In many cases, design specifications are based on the satisfaction of a set of property constraints. Recently, the novel paradigm "componentless design" was introduced by Shelley and El-Halwagi (Comput. Chem. Eng. 2000,24, 2081) to identify optimal graphical strategies for property-based problems. The essence of this approach is driven by tracking properties and not chemical components. Notwithstanding the usefulness of this graphical approach, it is limited to the simultaneous tracking of three properties. In this paper, we overcome this limitation by developing an algebraic approach for property integration through componentless design. Process constraints and stream characterization are described using bounds on intensive properties and flows. The problem of allocating streams is mapped into an equidimensional domain of dimensionless property operators. The specific mathematical structure of the set of operator constraints is exploited to develop a constraint-reduction algorithm, which provides rigorous bounds on the feasibility region. The result is an efficient algebraic procedure that identifies optimal allocation in the property-operator domain. The solution is then mapped back to the raw-property domain. To illustrate the applicability of the developed approach, a four-property case study is addressed using the devised algebraic procedure.