In the last decades, under the headings of “mutation strategies,” “evolvability,” or “soft inheritance,” many ideas have been advanced on mechanisms assumed to promote innovative evolution beyond what one may anticipate from the classical model of random mutation and selection. Many population geneticists find these ideas superficially seducing but mathematically unfounded. While agreeing with the need to critically evaluate such proposals in the light of population genetics, I will argue that population geneticists are not immune to criticism. For instance, the “infinite site model” introduced by Kimura makes the unrealistic assumption that any neutral mutation arises only once during a neutral fixation episode, which leads, I propose, to an underestimation of the neutral fixation rates in large populations. Critical parameters such as mutation and recombination rates, effective population sizes or beneficial/deleterious mutation ratios are assigned convenient values, which may seem ad hoc to people outside the field. The lack of concern for the subtleties of genetic mechanisms is also criticized. Phenomena such as compensatory mutations, recurrent mutations, hot spots, and polymorphism, which population geneticists treat in the mathematical context of neutral versus selective fixations, can instead be interpreted in terms of genetic mechanisms for producing complex mutational events. Finally, single nucleotide substitutions are often treated as the quasi-exclusive source of variations, yet they cannot help much once the genes are optimized with respect to these substitutions. I suggest that population geneticists should invest more effort in refining the numerical values of the critical parameters used in their models. They should take into account the recent proposals on how mutations arise. They should also pay more attention to phenotypic variations, and develop criteria to discriminate between proposed evolutionary mechanisms that can actually work, and others that cannot.