  We consider the problem of improving the effective potential in mass
independent schemes, as e.g. the $\MSbar$ or $\DRbar$ renormalization scheme,
in the presence of an arbitrary number of fields with $\phi$-dependent masses
$M_i(\phi_c)$. We use the decoupling theorem at the scales $\mu_i=M_i(\phi_c)$
such that the matching between the effective (low energy) and complete (high
energy) one-loop theories contains no thresholds. We find that for any value of
$\phi_c$, there is a convenient scale $\mu^*\equiv\min_i\{M_i(\phi_c)\}$, at
which the loop expansion has the best behaviour and the effective potential has
the least $\mu$-dependence. Furthermore, at this scale the effective potential
coincides with the (improved) tree-level one in the effective field theory. The
decoupling method is explicitly illustrated with a simple Higgs-Yukawa model,
along with its relationship with other decoupling prescriptions and with
proposed multi-scale renormalization approaches. The procedure leads to a nice
suppression of potentially large logarithms and can be easily adapted to
include higher-loop effects, which is explicitly shown at the two-loop level.
