In this paper we skim the true phenomenological requirements behind the concept of inflationary squeezing. We argue that all that is required is that at horizon re-entry the fluctuations form standing waves with the correct temporal phase (specifically, sine waves). We quantify this requirement and relate it to the initial conditions fed into the radiation dominated epoch by whatever phase of the Universe produced the fluctuations. The only relevant quantity turns out to be the degree of suppression of the momentum, p, of the fluctuations, y, which we measure by σ~ ω2 |y|2/|p|2. Even though σ equals the squeezing parameter, s, in the case of inflation and bimetric varying speed of light scenarios, this is not true in general, specifically in some bouncing Universe models. It is also not necessary to produce a large σ at the end of the primordial phase: it is enough that σ be not too small. This is the case with scenarios based on modified dispersion relations (MDR) emulating the dispersion relations of Horava-Lifshitz theory, which produce σ~ 1, enough to comply with the observational requirements. Scenarios based on MDR leading to a slightly red spectrum are also examined, and shown to satisfy the observational constraints.