The current capacity of computers makes it possible to perform simulations of small systems with portable, explicit-solvent potentials achieving high degree of accuracy. However, simplified models must be employed to exploit the behaviour of large systems or to perform systematic scans of smaller systems. While powerful algorithms are available to facilitate the sampling of the conformational space, successful applications of such models are hindered by the availability of simple enough potentials able to satisfactorily reproduce known properties of the system. We develop an interatomic potential to account for a number of properties of proteins in a computationally economic way. The potential is defined within an all-atom, implicit solvent model by contact functions between the different atom types. The associated numerical values can be optimised by an iterative Monte Carlo scheme on any available experimental data, provided that they are expressible as thermal averages of some conformational properties. We test this model on three different proteins, for which we also perform a scan of all possible point mutations with explicit conformational sampling. The resulting models, optimised solely on a subset of native distances, not only reproduce the native conformations within a few Angstroms from the experimental ones, but show the cooperative transition between native and denatured state and correctly predict the measured free--energy changes associated with point mutations. Moreover, differently from other structure-based models, our method leaves a residual degree of frustration, which is known to be present in protein molecules.