Preventing unintentional leakage of information about the training set has high relevance for many machine learning tasks, such as medical image segmentation. While differential privacy (DP) offers mathematically rigorous protection, the high output dimensionality of segmentation tasks prevents the direct application of state-of-the-art algorithms such as Private Aggregation of Teacher Ensembles (PATE). In order to alleviate this problem, we propose to learn dimensionality-reducing transformations to map the prediction target into a bounded lower-dimensional space to reduce the required noise level during the aggregation stage. To this end, we assess the suitability of principal component analysis (PCA) and autoencoders. We conclude that autoencoders are an effective means to reduce the noise in the target variables.