We theoretically reveal a new mechanism of light amplification in graphene under the conditions of interband population inversion. It is enabled by the indirect interband transitions, with the photon emission preceded or followed by the scattering on disorder. The emerging contribution to the optical conductivity, which we call the interband Drude conductivity, appears to be negative for the photon energies below the double quasi-Fermi energy of pumped electrons and holes. We find that for the Gaussian correlated distribution of scattering centers, the real part of the net Drude conductivity (interband plus intraband) can be negative in the terahertz and near-infrared frequency ranges, while the radiation amplification by a single graphene sheet can exceed 2.3%.Graphene under the conditions of interband pumping has attracted considerable interest [1] due to the rich physics including nonlinear photoresponse [2], collinear relaxation and recombination [3], anomalous carrier diffusion [4], and self-excitation of surface plasmons [5]. The emergence of population inversion [6-8] and negative interband dynamic conductivity in pumped graphene enables the amplification of radiation, particularly, in the terahertz (THz) range [9]. The experimental observation of coherent radiation amplification [10,11] supports an idea of graphene-based THz-laser [12,13]. Its full-scale realization faces, however, a number of challenges. First, the coefficient of the interband amplification by a clean layer of pumped graphene cannot exceed 2.3% [9], which is inseparably linked with the universal optical conductivity of graphene [14]. Second, the radiation amplification associated with the direct interband electron transitions competes with the intraband Drude absorption [15,16] which is inversely proportional to the frequency squared. The intraband photon absorption can be assisted by the processes of electron-phonon [17], electron-impurity, and carrier-carrier [18,19] scattering.Considering the optical conductivity of direct-gap semiconductors, one typically accounts only for direct interband and indirect intraband electron transitions (the latter shown in Fig. 1A). There also exist indirect interband transitions, with the photon absorption (or emission) followed (or preceded) by the disorder (impurity or phonon) scattering (Fig.