  We propose CFT descriptions of the D1/D5 system in a class of freely acting
Z_2 orbifolds/orientifolds of type IIB theory, with sixteen unbroken
supercharges. The CFTs describing D1/D5 systems involve N=(4,4) or N=(4,0)
sigma models on $(R^3\times S^1\times T^4\times (T^4)^N/S_N)/Z_2$, where the
action of Z_2 is diagonal and its precise nature depends on the model. We also
discuss D1(D5)-brane states carrying non-trivial Kaluza-Klein charges. The
resulting multiplicities for two-charge bound states are shown to agree with
the predictions of U-duality. We raise a puzzle concerning the multiplicities
of three-charge systems, which is generically present in all vacuum
configurations with sixteen unbroken supercharges studied so far, including the
more familiar type IIB on K3 case: the constraints put on BPS counting formulae
by U-duality are apparently in contradiction with any CFT interpretation. We
argue that the presence of RR backgrounds appearing in the symmetric product
CFT may provide a resolution of this puzzle.
