Third minima in actinides - do they exist?

We study the existence of third, hyperdeformed minima in a number of even-even Th, U and Pu nuclei using the Woods-Saxon microscopic-macroscopic model that very well reproduces first and second minima and fission barriers in actinides. Deep ($3 \div 4$ MeV) minima found previously by \'Cwiok et al. are found spurious after sufficiently general shapes are included. Shallow third wells may exist in $^{230,232}$Th, with IIIrd barriers $\le$ 200 and 330 keV (respectively). Thus, a problem of qualitative discrepancy between microscopic-macroscopic and selfconsistent predictions is resolved. Now, an understanding of experimental results on the apparent third minima in uranium becomes an issue.