Whether ad hoc or justified by theoretical arguments, the constancy of the dimensionless dissipation parameter, defined in terms of the turbulence kinetic energy, its dissipation rate and the length scale of the energetic motions, has been the basis of many acclaimed turbulence theories and models. The growing body of evidence that, although this postulate holds in extensive regions of canonical flows, it is invalid in other regions of the same flows will be reviewed first. This will be followed by a review of recent evidence that the dissipation parameter varies significantly in non-canonical flows, including multi-structure turbulence, which is generated by multiple, distinct production mechanisms. In several, but not all, cases, the dissipation parameter is seen to be inversely proportional to the local turbulence Reynolds number.