A method is introduced or demonstrating that a category has no minimal generating class. This technique is then utilized to show that various categories have no minimal generating classes. These categories include the completely Hausdorff spaces and the regular completely Hausdorff spaces. They also include the categories of spaces which can be embedded in m-bounded Hausdorff spaces, in m-bounded T3spaces, in m-bounded completely Hausdorff spaces, in regular m-bounded completely Hausdorff spaces and products of KC spaces.