  We discuss renormalisation group improvement of the effective potential both
in general and in the context of $O(N)$ scalar $\p^4$ and the Standard Model.
In the latter case we find that absolute stability of the electroweak vacuum
implies that $m_H\geq 1.95m_t-189~GeV$, for $\as (M_Z) = 0.11$. We point out
that the lower bound on $m_H$ {\it decreases\/} if $\as (M_Z)$ is increased.
