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Breast tumor segmentation is a critical task in computer-aided diagnosis (CAD) systems for breast cancer detection because accurate tumor size, shape and location are important for further tumor quantification and classification. However, segmenting small tumors in ultrasound images is challenging, due to the speckle noise, varying tumor shapes and sizes among patients, and the existence of tumor-like image regions. Recently, deep learning-based approaches have achieved great success for biomedical image analysis, but current state-of-the-art approaches achieve poor performance for segmenting small breast tumors. In this paper, we propose a novel deep neural network architecture, namely Enhanced Small Tumor-Aware Network (ESTAN), to accurately and robustly segment breast tumors. ESTAN introduces two encoders to extract and fuse image context information at different scales and utilizes row-column-wise kernels in the encoder to adapt to breast anatomy. We validate the proposed approach and compare it to nine state-of-the-art approaches on three public breast ultrasound datasets using seven quantitative metrics. The results demonstrate that the proposed approach achieves the best overall performance and outperforms all other approaches on small tumor segmentation.