  We study the effect of a central mass concentration (CMC) on the secular
evolution of a barred disc galaxy. Unlike previous studies, we use fully
self-consistent 3D $N$-body simulations with live haloes, which are known to be
important for bar evolution. The CMC is introduced gradually, to avoid
transients. In all cases where the mass of the CMC is of the order of, or more
than, a few per cent of the mass of the disc, the strength of the bar decreases
noticeably. The amount of this decrease depends strongly on the bar type. For
the same CMC, bars with exponential surface-density profile, which formed in a
disk-dominated galaxy (MD-type bars), can be totally destroyed, while strong
bars with a flat surface-density profile, whose evolution is largely due to the
halo (MH-type bars), witness only a decrease of their strength. This decrease
occurs simultaneously from both the innermost and outermost parts of the bar.
The CMC has a stronger effect on the Fourier components of higher azimuthal
wave number $m$, leading to fatter and/or less rectangular bars. Furthermore,
the CMC changes the side-on outline from peanut-shaped to boxy or, for massive
CMCs, to elliptical. Similarly, side-on initially boxy outlines can be
destroyed. The CMC also influences the velocity dispersion profiles. Most of
the decrease of the bar strength occurs while the mass of the CMC increases and
it is accompanied by an increase of the pattern speed. In all our simulations,
the mass of the CMC necessary in order to destroy the bar is at least several
per cent of the mass of the disc. This argues that observed super-massive black
holes are not likely to destroy pre-existing bars.
