Melting points in mixtures of a crystallizable polymer with a low-molar-mass diluent depend on both, the diluent fraction and the crystal thickness. A differentiation of the two factors can be achieved by temperature-dependent SAXS experiments. A corresponding study, complemented by DSC, dilatometry, microscopy and AFM-imaging, was carried out for mixtures of a poly(ethylene-co-octene) with n-C16H34, c-C16H32 and methyl-anthracene, respectively. All diluents lead for a constant crystal thickness to melting point depressions in agreement with Raoult's law. On the other hand, the effect of the diluents on the thickness of the crystals formed at a fixed crystallization temperature varies. While in the presence of the two alkanes thicker crystals form, no effect arises for the methyl-anthracene--as was previously found for the octene-co-units. We consider these observations as a further support for our view that polymer crystallization follows a multi-stage route which includes a passage through an intermediate mesomorphic phase. Under such conditions crystal thicknesses would only be affected if the diluent is still present in the mesomorphic phase and stay invariant if the diluent molecules are already rejected when this intermediate phase forms.