  A correction to the nuclear functional is proposed in order to improve the
density of states around the Fermi surface. The induced effect of this
correction is to produce a surface-peaked effective mass, whose mean value can
be tuned to get closer to 1 for the states close to the Fermi energy. In this
work we study the effect of the correction term on global properties of nuclei
such as the density of states in $^{40}$Ca and $^{208}$Pb, pairing and specific
heat at low temperature in $^{120}$Sn. In the latter application, an explicit
temperature-dependent form of the correction term is employed and it is shown
that the critical temperature is reduced by 40-60~keV.
