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MRI scans appearance significantly depends on scanning protocols and, consequently, the data-collection institution. These variations between clinical sites result in dramatic drops of CNN segmentation quality on unseen domains. Many of the recently proposed MRI domain adaptation methods operate with the last CNN layers to suppress domain shift. At the same time, the core manifestation of MRI variability is a considerable diversity of image intensities. We hypothesize that these differences can be eliminated by modifying the first layers rather than the last ones. To validate this simple idea, we conducted a set of experiments with brain MRI scans from six domains. Our results demonstrate that 1) domain-shift may deteriorate the quality even for a simple brain extraction segmentation task (surface Dice Score drops from 0.85-0.89 even to 0.09); 2) fine-tuning of the first layers significantly outperforms fine-tuning of the last layers in almost all supervised domain adaptation setups. Moreover, fine-tuning of the first layers is a better strategy than fine-tuning of the whole network, if the amount of annotated data from the new domain is strictly limited.