  The results by A.S. Barabash [Phys. Rev. {\bf C 81}, 035501 (2010)] are shown
to be incomplete. Tellurium data sets were reanalyzed using the best practices
of ENSDF evaluations. Present analysis indicates much higher value for the
2$\nu$-mode half-life time in $^{128}$Te and the corresponding ratio of
$^{128,130}$Te half-lives. These values imply the $T^{2 \nu}_{1/2}$ $\sim$
$\frac{1}{E^{8}}$ $\beta\beta$-decay transition energy trend that is consistent
with the two-nucleon mechanism of $\beta\beta$(2$\nu$)-decay.
