We report on numerical results from an independent formalism to describe the quasi-equilibrium structure of nonsynchronous binary neutron stars in general relativity. This is an important independent test of controversial numerical hydrodynamic simulations which suggested that nonsynchronous neutron stars in a close binary can experience compression prior to the last stable circular orbit. We show that, for compact enough stars the interior density increases slightly as irrotational binary neutron stars approach their last orbits. The magnitude of the effect, however, is much smaller than that reported in previous hydrodynamic simulations.