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Deep learning has made a breakthrough in medical image segmentation in recent years due to its ability to extract high-level features without the need for prior knowledge. In this context, U-Net is one of the most advanced medical image segmentation models, with promising results in mammography. Despite its excellent overall performance in segmenting multimodal medical images, the traditional U-Net structure appears to be inadequate in various ways. There are certain U-Net design modifications, such as MultiResUNet, Connected-UNets, and AU-Net, that have improved overall performance in areas where the conventional U-Net architecture appears to be deficient. Following the success of UNet and its variants, we have presented two enhanced versions of the Connected-UNets architecture: ConnectedUNets+ and ConnectedUNets++. In ConnectedUNets+, we have replaced the simple skip connections of Connected-UNets architecture with residual skip connections, while in ConnectedUNets++, we have modified the encoder-decoder structure along with employing residual skip connections. We have evaluated our proposed architectures on two publicly available datasets, the Curated Breast Imaging Subset of Digital Database for Screening Mammography (CBIS-DDSM) and INbreast.