  Mejia-Rodriguez and Trickey recently proposed a procedure for removing the
explicit dependence of meta-GGA exchange-correlation energy functionals $E_{\rm
xc}$ on the kinetic energy density $\tau$. We present a simple modification to
this approach in which the exact Kohn-Sham $\tau$ is used as input for $E_{\rm
xc}$ but the functional derivative of $\tau$ with respect to the density
$\rho$, required to calculate the potential term $\int d^3r'\,\delta E_{\rm
xc}/\delta\tau({\bf r}')|_{\rho}\cdot
  \delta\tau({\bf r}')/\delta\rho({\bf r})$, is evaluated using an approximate
kinetic energy density functional. This ensures that the Kohn-Sham potential is
a local multiplicative function as opposed to the non-local potential of a
generalized Kohn-Sham approach. Electronic structure codes can be easily
modified to use the new method. We validate it by quantifying the accuracy of
the predicted lattice parameters, bulk moduli, magnetic moments and cohesive
energies of a large set of periodic solids. An unanticipated benefit of this
method is to gauge the quality of approximate kinetic energy functionals by
checking if the self-consistent solution is indeed at the variational minimum.
