Microcalcifications are small deposits of calcium that appear in mammograms as bright white specks on the soft tissue background of the breast. Microcalcifications may be a unique indication for Ductal Carcinoma in Situ breast cancer, and therefore their accurate detection is crucial for diagnosis and screening. Manual detection of these tiny calcium residues in mammograms is both time-consuming and error-prone, even for expert radiologists, since these microcalcifications are small and can be easily missed. Existing computerized algorithms for detecting and segmenting microcalcifications tend to suffer from a high false-positive rate, hindering their widespread use. In this paper, we propose an accurate calcification segmentation method using deep learning. We specifically address the challenge of keeping the false positive rate low by suggesting a strategy for focusing the hard pixels in the training phase. Furthermore, our accurate segmentation enables extracting meaningful statistics on clusters of microcalcifications.