Using the wave-vector analysis of the jellium exchange-correlation surface energy, we show that the PBEint generalized gradient approximation (GGA) of Fabiano et al.[Phys. Rev. B 82, 113104 (2010)] is one of the most accurate density functionals for jellium surfaces, being able to describe both exchange and correlation parts of the surface energy, without error compensations. We show that the stabilized jellium model allows us to achieve a realistic description of the correlation surface energy of simple metals at any wave vector k. The PBEint correlation is then used to construct a meta-GGA correlation functional, modifying the one-electron self-correlation-free Tao-Perdew-Staroverov-Scuseria (TPSS) one. We find that this new functional (named JS) performs in agreement with fixed-node diffusion Monte Carlo estimates of the jellium surfaces, and is accurate for spherical atoms and ions of different spin …