Convolutional Neural Networks (CNNs) are brain-inspired computational models designed to recognize patterns. Recent advances demonstrate that CNNs are able to achieve, and often exceed, human capabilities in many application domains. Made of several millions of parameters, even the simplest CNN shows large model size. This characteristic is a serious concern for the deployment on resource-constrained embedded-systems, where compression stages are needed to meet the stringent hardware constraints. In this paper, we introduce a novel accuracy-driven compressive training algorithm. It consists of a two-stage flow: first, layers are sorted by means of heuristic rules according to their significance; second, a modified stochastic gradient descent optimization is applied on less significant layers such that their representation is collapsed into a constrained subspace. Experimental results demonstrate that our approach achieves remarkable compression rates with low accuracy loss (<1%).