Accurate and fast segmentation of nuclei in histopathological images plays a crucial role in cancer research for detection and grading, as well as personal treatment. Despite the important efforts, current algorithms are still suboptimal in terms of speed, adaptivity and generalizability. Popular Deep Convolutional Neural Networks (DCNNs) have recently been utilized for nuclei segmentation, outperforming traditional approaches that exploit color and texture features in combination with shallow classifiers or segmentation algorithms. However, DCNNs need large annotated datasets that require extensive amount of time and expert knowledge. In addition, segmentation results obtained by either traditional or DCNN approaches often require a post-processing step to separate cluttered nuclei. In this paper, we propose a computationally efficient nuclei segmentation framework based on DCNNs exhibiting an encoding-decoding structure. We use a partially-annotated dataset and develop an effective training solution. We also use a weighted background model for network to give more importance to borders of nuclei to overcome the problem of clutters. The abolition of any pre-processing or post-processing step without any compromise on the performance leads to a fast and parameter-free system, which presents important advantages with respect to state-of-the-art.