  The charged Banados-Teitelboim-Zanelli (BTZ) black hole is plagued by several
pathologies: a) Presence of divergent boundary terms in the action, hence of a
divergent black hole mass; b) Once a finite, renormalized, mass M is defined
black hole states exist for arbitrarily negative values of M; c) There is no
upper bound on the charge Q. We show that these pathological features are an
artifact of the renormalization procedure. They can be completely removed by
using an alternative renormalization scheme leading to a different definition
M_0 of the black hole mass, which is the total energy inside the horizon. The
new mass satisfies a BPS-like bound M_0\ge (\pi/2)Q^2 and the heat capacity of
the hole is positive. We also discuss the black hole thermodynamics that arises
when M_0 is interpreted as the internal energy of the system. We show, using
three independent approaches (black hole thermodynamics, Einstein equations,
Euclidean action formulation) that M_0 satisfies the first law if a term
describing the mechanical work done by the electrostatic pressure is
introduced.
