Multisine signals are used in many applications like fast estimation of frequency response function, as well as in a variety of other fields. Synthesis of a low crest factor (CF) multisine waveform with the given amplitude spectrum depends on initial phases of its components. Approaches for finding good initial phases can be divided into two classes: analytical, direct formula calculations and use of numerical iterative search algorithms. In some cases, the direct formula calculation is used as a starting point for the further iterative search. This paper presents both, new direct formulas and an improved iterative search algorithm to synthesize arbitrary spectrum multisine with the lowest CF. Comparison with the results of earlier methods proves the positive effect of proposed modifications.DOI: http://dx.doi.org/10.5755/j01.eie.23.2.18001