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Mini-jets, created by perturbative hard QCD collisions at moderate energies, can represent a significant portion of the total multiplicity of a heavy-ion collision event. Since their transverse momenta are initially larger than the typical saturation scale describing the bulk of the equilibrating QGP, their typical stopping distances are larger than the usual hydrodynamization time, so they do not in general hydrodynamize at the same pace than the bulk of the collision. Therefore, in general mini-jets cannot be described solely by a unique pre-equilibrium stage that bridges the initial, over-occupied glasma state, with the hydrodynamical evolution. In this work we make use of a new concurrent mini-jet+hydrodynamic framework in which the properties of the hydrodynamically evolving QGP are modified due to the injection of energy and momentum from the mini-jets. We study the system for different choices of the minimum transverse momentum associated to mini-jet production. In order to achieve a realistic description of charged particle multiplicity, the amount of entropy associated to the low-$x$ initial state needs to be reduced. Moreover, the fact that the injected momentum from the randomly oriented mini-jets is not correlated with the spatial gradients of the system reduces overall flow, and the value of the QGP transport coefficients needs to be reduced accordingly. They are an important new source of fluctuations, resulting in a spikier, notably modified hydrodynamical evolution. We discuss the impact of the mini-jets on a number of observables, such as $p_T$ spectra and $p_T$-differential flow $v_n$ for a wide range of centrality classes. In contrast to elliptic, triangular or quadrangular flow, we find that directed flow, $v_1$, has the strongest potential to discriminate between different mini-jet production rates.