An effective potential evaluated perturbatively can possess false minima, artefacts of the approximation method itself. The author attempts to provide evidence that within pure perturbation theory it is almost impossible to conclude whether or not a perturbative minimum actually approximates a true minimum. On the other hand, renormalisation group (RG) methods can provide answers on the falseness of a minimum (but generally cannot validate a minimum). The general remarks are illustrated by studying massless phi ⁴ to a two-loop level. It is shown that RG methods different from those of Coleman and Weinberg must be employed to establish the falseness of a one-loop minimum which this theory possesses.