Since the early days of helioseismology, adiabatic models have shown their limits for a precise fitting of individual oscillation frequencies. This discrepancy, which also exists for solar-type stars, is known to originate near the surface superadiabatic convective region where the interaction between oscillations and convection is likely to have a large effect on the frequencies. We present an asteroseismic study to address the adequacy of time-dependent convection (TDC) non-adiabatic models to better reproduce the observed individual frequencies. We select, for this purpose, three solar-like stars, in addition to the Sun, to which we fit the observed frequencies in a grid of TDC non-adiabatic models. The best model selection is done by applying a maximum likelihood method. The results are compared to pure adiabatic and near-surface corrected adiabatic models. We show that, first, TDC models give very good agreement for the mode frequencies and average lifetimes. In the solar case, the frequency discrepancy is reduced to <1.75 μHz over 95 per cent of the modes considered. Secondly, TDC models give an asteroseismic insight into the usually unconstrained ad hoc stellar parameters, such as the mixing-length parameter αMLT.