The demand for the deployment of deep neural networks (DNN) on resource-constrained Edge platforms is ever increasing. Today's DNN accelerators support mixed-precision computations to enable reduction of computational and storage costs but require networks with precision at variable granularity, i.e., network, layer or kernel level. However, the problem of granular precision assignment is challenging due to an exponentially large search space and efficient methods for such precision assignment are lacking. To address this problem, we introduce the iterative mixed-precision quantization (IMPQ) framework to allocate precision at variable granularity. IMPQ employs a sensitivity metric to order the weight/activation groups in terms of the likelihood of misclassifying input samples due to its quantization noise. It iteratively reduces the precision of the weights and activations of a pretrained full-precision network starting with the least sensitive group. Compared to state-of-the-art methods, IMPQ reduces computational costs by 2×-to-2.5× for compact networks such as MobileNet-V1 on ImageNet with no accuracy loss. Our experiments reveal that kernel-wise granular precision assignment provides 1.7× higher compression than layer-wise assignment.