We present a simple and effective strategy for simulating the phase coexistence of off-lattice polymer-solvent mixtures when the solvent-rich phase contains negligible polymer. Under conditions sufficiently far from the solution critical point, an osmotic equilibrium is established between a pure solvent phase and a polymer-rich phase that produces a polymer-rich phase indistinguishable from the corresponding phase of the full binary mixture. Evaluation of the accuracy and reliability of the method is tested on a simple bead-spring model under both constant-pressure and constant-temperature conditions. A key advantage of the method over currently available techniques is that the insertion and deletion of chain molecules are not required. Though the method is illustrated for short, linear chains, it has even wider applicability for long, linear chains as well as for branched and networked chains, For many engineering applications, the method alone may suffice for simulating the relevant portion of the coexistence curve.