  We present long term evolutions of a single black hole of mass $M$ with the
BSSN system using pseudospectral methods. For our simulations we use the SGRID
code where the BSSN system is implemented in its standard second order in space
form. Previously we found that such simulations are quite unstable. The main
goal of this paper is to present two improvements which now allow us to evolve
for longer times. The first improvement is related to the boundary conditions
at the excised black hole interior. We now use a gauge condition that ensures
that all modes are going into the black hole, so that no boundary conditions
are needed at the excision surface. The second more significant improvement has
to do with our particular numerical method and involves filters based on
projecting the double Fourier expansions used for the angular dependence onto
Spherical Harmonics. With these two improvements it is now easily possible to
evolve for several thousand $M$. The only remaining limitation seems to be the
radiative outer boundary conditions used here. Yet this problem can be
ameliorated by pushing out the location of the outer boundary, which leads to
even longer run-times.
