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In this work, we propose a novel architecture for face age editing that can produce structural modifications while maintaining relevant details present in the original image. We disentangle the style and content of the input image and propose a new decoder network that adopts a style-based strategy to combine the style and content representations of the input image while conditioning the output on the target age. We go beyond existing aging methods allowing users to adjust the degree of structure preservation in the input image during inference. To this purpose, we introduce a masking mechanism, the CUstom Structure Preservation module, that distinguishes relevant regions in the input image from those that should be discarded. CUSP requires no additional supervision. Finally, our quantitative and qualitative analysis which include a user study, show that our method outperforms prior art and demonstrates the effectiveness of our strategy regarding image editing and adjustable structure preservation. Code and pretrained models are available at https://github.com/guillermogotre/CUSP.