  We study $N^2-1$ dimensional left-covariant differential calculi on the
quantum group $SL_q(N)$ for which the generators of the quantum Lie algebras
annihilate the quantum trace. In this way we obtain one distinguished calculus
on $SL_q(2)$ (which corresponds to Woronowicz' 3D-calculus on $SU_q(2)$) and
two distinguished calculi on $SL_q(3)$ such that the higher order calculi give
the ordinary differential calculus on $SL(2)$ and $SL(3)$, respectively, in the
limit $q\rightarrow 1$. Two new differential calculi on $SL_q(3)$ are
introduced and developed in detail.
