In this section, we want to give a number of applications of the constrained randomisation approach. If the constraints consist only of the Fourier amplitudes and the single time probability distribution, the iteratively refined, amplitude adjusted surrogates [30] discussed in Sec. 4.3 are usually sufficient if the end point artefact can be controlled and convergence is satisfactory. Even the slightest extension of these constraints makes it impossible to solve the inverse problem directly and we have to follow the more general combinatorial approach discussed in the previous section. The following examples are meant to illustrate how this can be carried out in practice.