When a linear polyethylene is blended with two homogeneous copolymers, of different comonomer content, the resulting ternary phase diagram shows three distinct regions of liquid-liquid phase separation. It is argued that we may usefully employ a ternary phase diagram to understand the degree of melt demixing occurring in some commercial polymers, such as linear low-density polyethylenes (LLDPEs), which are blends in themselves. Results obtained on blending LLDPEs with linear or randomly branched polyethylenes are presented, and it is shown that the observed phase behaviour may be interpreted as cloud point curves arising from sections through phase diagrams of ternary blend systems. The ternary phase diagram used in this work was originally determined experimentally for octene copolymers, but it is now shown to be equally applicable to butene copolymers.