  We present arguments for the existence of new black string solutions with
negative cosmological constant. These higher-dimensional configurations have no
dependence on the `compact' extra dimension, and their conformal infinity is
the product of time and $S^{d-3}\times R$ or $H^{d-3}\times R$. The
configurations with an event horizon topology $S^{d-2}\times S^1$ have a
nontrivial, globally regular limit with zero event horizon radius. We discuss
the general properties of such solutions and, using a counterterm prescription,
we compute their conserved charges and discuss their thermodynamics. Upon
performing a dimensional reduction we prove that the reduced action has an
effective $SL(2,R)$ symmetry. This symmetry is used to construct non-trivial
solutions of the Einstein-Maxwell-Dilaton system with a Liouville-type
potential for the dilaton in $(d-1)$-dimensions.
