  In this paper we reconsider recently derived bounds on $MeV$ tau neutrinos,
taking into account previously unaccounted for effects. We find that, assuming
that the neutrino life-time is longer than $O(100~sec)$, the constraint
$N_{eff}<3.6$ rules out $\nu_{\tau}$ masses in the range
$0.5~(MeV)<m_{\nu_\tau}<35~(MeV)$ for Majorana neutrinos and
$0.74~(MeV)<m_{\nu_\tau}<35~(MeV)$ for Dirac neutrinos. Given that the present
laboratory bound is 35 MeV, our results lower the present bound to $0.5$ and
$0.74$ for Majorana and Dirac neutrinos respectively.
