In the experimental identification of Tokamak equilibria from external magnetic measurements, the addition of integral constraints to the full equilibrium analysis provides extra information on the toroidal current distribution, improving the stability of the solution against measurement errors, and increasing the accuracy of its determination. It is shown that the use of the toroidal flux value measured by the diamagnetic loop as an additional constraint to the free-boundary equilibrium solver increases to four the number of independent parameters that can be identified in the current density profile, providing a more precise evaluation of the relative weight of the pressure and paramagnetic terms.