This work introduces the “Select and retrieve via direct up-sampling” network (SARDU-Net), a new method for model-free, data-driven quantitative MRI (qMRI) experiment design. SARDU-Net identifies informative measurements within lengthy acquisitions and reconstructs fully-sampled signals from a sub-protocol, without prior information on the MRI contrast. It combines two deep networks: a selector, which selects a signal sub-sample, and a predictor, which retrieves input signals. SARDU-Net can be run with standard computational resources and can increase the clinical appeal of qMRI. Here we demonstrate its potential on qMRI of prostate and spinal cord, two areas where fast acquisitions are key.