We propose a novel lightweight network for stereo estimation. Our network consists of a fully-convolutional densely connected neural network (FC-DCNN) that computes matching costs between rectified image pairs. Our FC-DCNN method learns expressive features and performs some simple but effective post-processing steps. The densely connected layer structure connects the output of each layer to the input of each subsequent layer. This network structure in addition to getting rid of any fully-connected layers leads to a very lightweight network. The output of this network is used in order to calculate matching costs and create a cost-volume. Instead of using time and memory-inefficient cost-aggregation methods such as semi-global matching or conditional random fields in order to improve the result, we rely on filtering techniques, namely median filter and guided filter. By computing a left-right consistency check we get rid of inconsistent values. Afterwards we use a watershed foreground-background segmentation on the disparity image with removed inconsistencies. This mask is then used to refine the final prediction. We show that our method works well for both challenging indoor and outdoor scenes by evaluating it on the Middlebury, KITTI and ETH3D benchmarks respectively.