Magnetic Resonance Fingerprinting (MRF) is a relatively new approach for simultaneously estimating multiple quantitative maps in one acquisition. Sequence optimisation for MRF can be a powerful tool in increasing the accuracy an precision of the quantitative results. Multi-component analysis in the MRF framework can distinguish multiple different tissues in one voxel such as myelin water and white matter which play an important role in monitoring progressive diseases such as multiple sclerosis. Using the estimation theoretic Cramér-Rao bound, optimisations of the acquisition sequences can be performed, that increase the precision of the resulting tissue maps. The effect of this optimisation has been confirmed using numerical simulations. Speed-ups in MRF are generated using significant undersampling of the k-space information. This results in spatially coherent undersampling artefacts, that generally is the dominating error source for regular $T_1$ and $T_2$ mapping. The undersampling artefacts can be predicted using a mathematical model leveraging on techniques from perturbation theory. Numerical simulations suggested that optimisations of the acquisition parameters are effective in reducing the undersampling error. This was confirmed using in vivo scans. The optimisations resulting from these two different models are easily implemented in future clinical practice.