  Dynamo models relying on the Babcock-Leighton mechanism are successful in
reproducing most of the solar magnetic field dynamical characteristics.
However, considering that such models operate only above a lower magnetic field
threshold, they do not provide an appropriate magnetic field regeneration
process characterizing a self-sustainable dynamo. In this work we consider the
existence of an additional \alpha-effect to the Babcock-Leighton scenario in a
mean-field axisymmetric kinematic numerical model. Both poloidal field
regeneration mechanisms are treated with two different strength-limiting
factors. Apart from the solar anti-symmetric parity behavior, the main solar
features are reproduced: cyclic polarity reversals, mid-latitudinal equatorward
migration of strong toroidal field, poleward migration of polar surface radial
fields, and the quadrature phase shift between both. Long-term variability of
the solutions exhibits lengthy periods of minimum activity followed by
posterior recovery, akin to the observed Maunder Minimum. Based on the analysis
of the residual activity during periods of minimum activity, we suggest that
these are caused by a predominance of the \alpha-effect over the
Babcock-Leighton mechanism in regenerating the poloidal field.
