We identify and analyze a major issue pertaining to all power-spectrum based texture synthesis algorithms – from Fourier synthesis to procedural noise algorithms like Perlin or Gabor noise – , namely, the oscillation of contrast (see Figures 1,2,3,7). One of our key contributions is to introduce a simple yet powerful descriptor of signals, the Spectrum of Variance (not to be confused with the PSD), which, to our surprise, has never been leveraged before. In this new framework, several issues get easy to understand measure and control, with new handles, as we illustrate. We finally show that fixing oscillation of contrast opens many doors to a more controllable authoring of stochastic texturing. We explore some of the new reachable possibilities such as constrained noise content and bridges towards very different families of look such as cellular patterns, points-like distributions or reaction-diffusion.