We show that the use of simple but adequate pseudopotential models and the Weeks-Chandler-Andersen approach to the liquid theory enables us to calculate the melting curves T m( p) for simple metals such as Na, K, Rb and Cs with a high precision when the thermodynamic properties of both solid and liquid phases are evaluated consistently. The agreement with experiment in the volume jumps in fusion is also well for small pressures p ≈ 0 but worsens when p rises which seems to indicate an inadequate desription of the equilibrium lattice defect thermodynamic contribution.