  We derive a general formula for the RG improved effective (Coleman-Weinberg)
potential for classically conformal models, applying it to several examples of
physical interest, and in particular a model of QCD coupled via quarks to a
colorless scalar field. The closed form expressions allow us to discuss the
range of validity of the effective potential as well as the issue of `large
logarithms' in a way different from previous such analyses. Remarkably, in all
examples considered, convexity of the effective potential is restored by the RG
improvement, or otherwise the potential becomes unstable. In the former case,
symmetry breaking becomes unavoidable due to the appearance of an infrared
barrier $\Lambda_{IR}$, which hints at a so far unsuspected link between
$\Lambda_{QCD}$ and the scale of electroweak symmetry breaking.
