On the basis of experimental batch-cell data, increasing short-chain branch density is found to reduce the cloud-point pressure of poly(ethylene-1-butene) solutions in propane, by as much as a factor of 3. This trend is captured by a SAFT approximation via an effective segment energy that depends on the branch density. Increasing branch density is found to decrease the effective segment energy and, hence, to make it closer to that of propane, which is consistent with the enhanced miscibility of branchy poly(ethylene-1-butenes) in propane.