The likelihood of a first-order liquid-liquid phase change in carbon from a mostly graphitic configuration to one that is more tetrahedral in character is explored. Liquid-phase changes in other materials are noted. Pertinent data on liquid carbon are reviewed and the model is briefly described. The model is consistent with a positive diamond-melting-line slope. Constraints on the strain energy between graphitic and diamondlike liquid clusters allow a phase diagram with a liquid-liquid transition and a graphite-liquid-liquid triple point. An upper limit on the strain energy is the constraint that the graphite melting line should have a reasonable curvature that agrees with melting-line data. The transformation of liquid structure from graphitic to diamondlike under compression significantly increases the compressibility.