  Numerical simulations and analytical models suggest that infinite cosmic
strings produce cosmic string loops of all sizes with a given power-law.
Precise estimations of the power-law exponent are still matter of debate while
numerical simulations do not incorporate all the radiation and back-reaction
effects expected to affect the network at small scales. Previously it has been
shown, using a Boltzmann approach, that depending on the steepness of the loop
production function and the gravitational back-reaction scale, a so-called
Extra Population of Small Loops (EPSL) can be generated in the loop number
density. We propose a framework to study the influence of this extra population
of small loops on the Stochastic Background of Gravitational Waves (SBGW). We
show that this extra population can have a significant signature at frequencies
higher than $H_0(\Gamma G\mu)^{-1}$ where $\Gamma$ is of order $50$ and $H_0$
is the Hubble constant. We propose a complete classification of the
gravitational wave power spectra expected from cosmic strings into four
classes, including the model of Blanco-Pillado, Olum and Shlaer and the model
of Lorenz, Ringeval and Sakellariadou. Finally we show that given the
uncertainties on the Polchinski-Rocha exponents, two hybrid classes of
gravitational wave power spectrum can be considered giving very different
predictions for the SBGW.
