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Deep learning methods have been shown to be effective for the automatic segmentation of structures and pathologies in medical imaging. However, they require large annotated datasets, whose manual segmentation is a tedious and time-consuming task, especially for large structures. We present a new method of partial annotations that uses a small set of consecutive annotated slices from each scan with an annotation effort that is equal to that of only few annotated cases. The training with partial annotations is performed by using only annotated blocks, incorporating information about slices outside the structure of interest and modifying a batch loss function to consider only the annotated slices. To facilitate training in a low data regime, we use a two-step optimization process. We tested the method with the popular soft Dice loss for the fetal body segmentation task in two MRI sequences, TRUFI and FIESTA, and compared full annotation regime to partial annotations with a similar annotation effort. For TRUFI data, the use of partial annotations yielded slightly better performance on average compared to full annotations with an increase in Dice score from 0.936 to 0.942, and a substantial decrease in Standard Deviations (STD) of Dice score by 22% and Average Symmetric Surface Distance (ASSD) by 15%. For the FIESTA sequence, partial annotations also yielded a decrease in STD of the Dice score and ASSD metrics by 27.5% and 33% respectively for in-distribution data, and a substantial improvement also in average performance on out-of-distribution data, increasing Dice score from 0.84 to 0.9 and decreasing ASSD from 7.46 to 4.01 mm. The two-step optimization process was helpful for partial annotations for both in-distribution and out-of-distribution data. The partial annotations method with the two-step optimizer is therefore recommended to improve segmentation performance under low data regime.