This paper presents both new analytical and new numerical solutions to the problem of generating waveforms exhibiting a low peak-to-peak factor. One important application of these results is in the generation of pseudo-white noise signals that are commonly uses in multi-frequency measurements. These measurements often require maximum signal-to-noise ratio while maintaining the lowest peak-to-peak excursion. The new synthesis scheme introduced in this paper uses the Discrete Fourier Transform (DFT) to generate pseudo-white noise sequence that theoretically has a minimized peak-to-peak factor, Fp-p. Unlike theoretical works in the literature, the method presented here is based in purely discrete mathematics, and hence is directly applicable to the digital synthesis of signals. With this method the shape of the signal can be controlled with about N parameters given N harmonic components. A different permutation of the same set of offset phases of the "source harmonics" creates an entirely different sequence.