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Fine-tuning a network which has been trained on a large dataset is an alternative to full training in order to overcome the problem of scarce and expensive data in medical applications. While the shallow layers of the network are usually kept unchanged, deeper layers are modified according to the new dataset. This approach may not work for ultrasound images due to their drastically different appearance. In this study, we investigated the effect of fine-tuning different layers of a U-Net which was trained on segmentation of natural images in breast ultrasound image segmentation. Tuning the contracting part and fixing the expanding part resulted in substantially better results compared to fixing the contracting part and tuning the expanding part. Furthermore, we showed that starting to fine-tune the U-Net from the shallow layers and gradually including more layers will lead to a better performance compared to fine-tuning the network from the deep layers moving back to shallow layers. We did not observe the same results on segmentation of X-ray images, which have different salient features compared to ultrasound, it may therefore be more appropriate to fine-tune the shallow layers rather than deep layers. Shallow layers learn lower level features (including speckle pattern, and probably the noise and artifact properties) which are critical in automatic segmentation in this modality.