  The regularized signum-Gordon potential has a smooth minimum and is linear in
the modulus of the field value for higher amplitudes. The Q-ball solutions in
this model are investigated. Their existence for charges large enough is
demonstrated. In three dimensions numerical solutions are presented and the
absolute stability of large Q-balls is proved. It is also shown, that the
solutions of the regularized model approach uniformly the solution of the
unregularized signum-Gordon model. From the stability of Q-balls in the
regularized model follows the stability of the solutions in the original
theory.
