While the debate on the existence of 'directed', 'Cairnsian', 'adaptive' or 'post-selection' mutations still continues, the suggestion that such a feature will be strongly advantageous seems to be uncritically accepted. We modelled competition in a chemostat with the substrate alternating between a 'normal' and an 'alternative' nutrient. Simulations involving genotypes (1) with inducible operon for alternative substrate, (2) without any gene for the alternative substrate, (3) with a cryptic gene for the alternative substrate and the ability to bring about a directed mutation and (4) with a cryptic gene having mutational hotspot showed that a directed mutation conferred little selective advantage. The widely held belief is thus challenged and we need to look into the directed-mutation controversy with a new insight.