We present data from high-resolution numerical simulations of the Navier Stokes-alpha and the Leray-a models for two-dimensional turbulence. It was shown previously ( Lunasin et al 2007 J. Turbul. 8 30) that for wavenumbers k such that k alpha >> 1, the energy spectrum of the smoothed velocity field for the two-dimensional Navier-Stokes-alpha (NS-alpha) model scales as k(-7). This result is in agreement with the scaling deduced by dimensional analysis of the flux of the conserved enstrophy using its characteristic time scale. We therefore hypothesize that the spectral scaling of any alpha-model in the sub-alpha spatial scales must depend only on the characteristic time scale and dynamics of the dominant cascading quantity in that regime of scales. The data presented here, from simulations of the two-dimensional Leray-alpha model, confirm our hypothesis. We show that for ka >> 1, the energy spectrum for the two-dimensional Leray-alpha scales as k(-5), as expected by the characteristic time scale for the flux of the conserved enstrophy of the Leray-alpha model. These results lead to our conclusion that the dominant directly cascading quantity of the model equations must determine the scaling of the energy spectrum.