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We describe a search-free resizing framework that can further improve the rate-distortion tradeoff of recent learned image compression models. Our approach is simple: compose a pair of differentiable downsampling/upsampling layers that sandwich a neural compression model. To determine resize factors for different inputs, we utilize another neural network jointly trained with the compression model, with the end goal of minimizing the rate-distortion objective. Our results suggest that "compression friendly" downsampled representations can be quickly determined during encoding by using an auxiliary network and differentiable image warping. By conducting extensive experimental tests on existing deep image compression models, we show results that our new resizing parameter estimation framework can provide Bj{\o}ntegaard-Delta rate (BD-rate) improvement of about 10% against leading perceptual quality engines. We also carried out a subjective quality study, the results of which show that our new approach yields favorable compressed images. To facilitate reproducible research in this direction, the implementation used in this paper is being made freely available online at: https://github.com/treammm/ResizeCompression.