The intrinsic level-density parameters in natural radioactive nuclei, which emit alpha particles, have been extracted within a microscopic formalism based on the BCS model with inclusion of pairing interaction. Then, total level-density parameters considering the collective effects are obtained. In addition, the level-density parameter excess of total level-density parameter compared to the intrinsic level-density parameter as a function of excitation energy has been determined for each nucleus. A cusp in the level-density parameter excess is observed at energies about neutron binding energy for prolate deformed nuclei with [Formula: see text]. However, the level-density parameter excess behavior is quite incremental for the considered nuclei with [Formula: see text].