The recently popular deep neural networks (DNNs) have a significant effect on the improvement of segmentation accuracy from various perspectives, including robustness and completeness in comparison to conventional methods. We determined that the naive U-Net has some lacks in specific perspectives and there is high potential for further enhancements on the model. Therefore, we employed some modifications in different folds of the U-Net to overcome this problem. Based on the probable opportunity for improvement, we develop a novel architecture by using an alternative feature extractor in the encoder of U-Net and replacing the plain blocks with residual blocks in the decoder. This alteration makes the model superconvergent yielding improved performance results on two challenging optical microscopy image series: a phase-contrast dataset of our own (MDA-MB-231) and a brightfield dataset from a well-known challenge (DSB2018). We utilized the U-Net with pretrained ResNet-18 as the encoder for the segmentation task. Hence, following the modifications, we redesign a novel skip-connection to reduce the semantic gap between the encoder and the decoder. The proposed skip-connection increases the accuracy of the model on both datasets. The proposed segmentation approach results in Jaccard Index values of 85.0% and 89.2% on the DSB2018 and MDA-MB-231 datasets, respectively. The results reveal that our method achieves competitive results compared to the state-of-the-art approaches and surpasses the performance of baseline approaches.