Experimental melting temperatures and associated latent heats of size-selected sodium clusters are analyzed in the frame of a two-state model of melting. The strong variations of these quantities as a function of size make clusters an excellent benchmark for testing speculative ideas about melting. The relation between cohesive energy of clusters and their latent heat of melting is demonstrated, and a correlation between cohesive energy and vibrational frequency in the solid state is found. It is shown that this relation may throw light on the enthalpy-entropy compensation, which is observed in a variety of systems undergoing a first-order phase transition. A relation is established between the Lindemann melting criterion, the variation of the vibrational frequency with the cohesive energy, and the enthalpy-entropy compensation.