The concept of compressing deep Convolutional Neural Networks (CNNs) is essential to use limited computation, power, and memory resources on embedded devices. However, existing methods achieve this objective at the cost of a drop in inference accuracy in computer vision tasks. To address such a drawback, we propose a framework that leverages knowledge distillation along with customizable block-wise optimization to learn a lightweight CNN structure while preserving better control over the compression-performance tradeoff. Considering specific resource constraints, e.g., floating-point operations per second (FLOPs) or model-parameters, our method results in a state of the art network compression while being capable of achieving better inference accuracy. In a comprehensive evaluation, we demonstrate that our method is effective, robust, and consistent with results over a variety of network architectures and datasets, at negligible training overhead. In particular, for the already compact network MobileNet_v2, our method offers up to 2x and 5.2x better model compression in terms of FLOPs and model-parameters, respectively, while getting 1.05% better model performance than the baseline network.