We investigate the asymptotic scaling of the growth rate and of the characteristic layer width of reduced-MHD tearing modes occurring in thin current sheets when reconnection depends on two non-ideal parameters. For this purpose, we use a new multi-precision finite difference eigensolver. The viscous-resistive regime, the warm-resistive regime that includes both resistivity and electron temperature effects, the warm-inertial regime in which a finite electron inertia replaces resistivity in allowing reconnection, and the inertial-resistive regime that includes both electron inertia and resistivity are investigated. Previous analytical results of the first three regimes are recovered. For all regimes, the scalings of the width of the reconnecting layer are provided in the different limits of the wavelength spectrum, and general estimates for the fastest growing modes are obtained and generalized to different magnetic equilibria. Implications for the disruption of evolving current sheets are discussed.

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