A new, radical CNN design approach is introduced, considering the reduction of the total computational load during inference. This is achieved by a new holistic intervention on both the CNN architecture and the training procedure, which targets to the parsimonious inference by learning to exploit or remove the redundant capacity of a CNN architecture. This is accomplished, by the introduction of a new structural element that can be inserted as an addon to any contemporary CNN architecture, whilst preserving or even improving its recognition accuracy.