  I calculate the mixed threetangle $\tau_3[\rho]$ for the reduced density
matrices of the four-qubit representant states found in Phys. Rev. A {\bf 65},
052112 (2002). In most of the cases, the convex roof is obtained, except for
one class, where I provide with a new upper bound, which is assumed to be very
close to the convex roof. I compare with results published in Phys. Rev. Lett.
{\bf 113}, 110501 (2014). Since the method applied there usually results in
higher values for the upper bound, in certain cases it can be understood that
the convex roof is obtained exactly, namely when the zero-polytope where
$\tau_3$ vanishes shrinks to a single point.
