Very often the existence of charge and colour breaking minima in the MSSM is checked by using analytical conditions. I discuss the assumptions which enter these conditions and show that this ansatz is likely to miss dangerous CCB minima. Afterwards, I introduce the tool Vevacious which makes a fully numerical check of the stability of the
one-loop effective potential. The consequences for regions with the correct Higgs mass and light staus or stops in the constrained MSSM are discussed. Finally, it is shown that also thermal corrections to the potential are important when studying the natural MSSM. This affects also best-fit and benchmark points proposed in literature.
