Deep learning segmentation relies heavily on labeled data, but manual labeling is laborious and time-consuming, especially for volumetric images such as brain magnetic resonance imaging (MRI). While recent domain-randomization techniques alleviate the dependency on labeled data by synthesizing diverse training images from label maps, they offer limited anatomical variability when very few label maps are available. Semi-supervised self-training addresses label scarcity by iteratively incorporating model predictions into the training set, enabling networks to learn from unlabeled data. In this work, we combine domain randomization with self-training to train three-dimensional skull-stripping networks using as little as a single labeled example. First, we automatically bin voxel intensities, yielding labels we use to synthesize images for training an initial skull-stripping model. Second, we train a convolutional autoencoder (AE) on the labeled example and use its reconstruction error to assess the quality of brain masks predicted for unlabeled data. Third, we select the top-ranking pseudo-labels to fine-tune the network, achieving skull-stripping performance on out-of-distribution data that approaches models trained with more labeled images. We compare AE-based ranking to consistency-based ranking under test-time augmentation, finding that the AE approach yields a stronger correlation with segmentation accuracy. Our results highlight the potential of combining domain randomization and AE-based quality control to enable effective semi-supervised segmentation from extremely limited labeled data. This strategy may ease the labeling burden that slows progress in studies involving new anatomical structures or emerging imaging techniques.