Optimization techniques can be used to design scan parameters for quantitative imaging. The Cramér-Rao Lower Bound (CRLB) is often used for such designs, but it only characterizes unbiased estimators. We propose an end-to-end approach to scan design that optimizes scan parameters with a particular estimator in mind. We compare CRLB-based and end-to-end scan designs in the context of myelin water imaging. The end-to-end scan design results in lower estimation error in simulation and an in vivo myelin water fraction (MWF) map with improved contrast. The proposed end-to-end scan design approach is thus a promising alternative to using the CRLB.