  We investigate spherically symmetric non topological solitons in
electrodynamics with a scalar field self interaction U ~|\psi| taken from the
complex signum-Gordon model. We find Q-balls for small absolute values of the
total electric charge Q, and Q-shells when |Q| is large enough. In both cases
the charge density exactly vanishes outside certain compact region in the three
dimensional space. The dependence of the total energy E of small Q-balls on the
total electric charge has the form E ~ |Q|^(5/6), while in the case of very
large Q-shells E ~ |Q|^(7/6).
