  We examine the properties of the Bethe Ansatz solvable two- and three-leg
spin-$S$ ladders. These models include Heisenberg rung interactions of
arbitrary strength and thus capture the physics of the spin-$S$ Heisenberg
ladders for strong rung coupling. The discrete values derived for the
magnetization plateaux are seen to fit with the general prediction based on the
Lieb-Schultz- Mattis theorem. We examine the magnetic phase diagram of the
spin-1 ladder in detail and find an extended magnetization plateau at the
fractional value $<M > = {1/2}$ in agreement with the experimental observation
for the spin-1 ladder compound BIP-TENO.
