  The properties of two quantum spin chain materials, K$_2$CuSO$_4$Cl$_2$ and
K$_2$CuSO$_4$Br$_2$, are studied by a variety of experimental techniques,
including bulk measurements, neutron spectroscopy and ESR. The hierarchy of
relevant terms in the magnetic Hamiltonian is established. It is shown that
these two compounds feature substantial Dzyaloshinskii-Moriya (DM) interactions
that are uniform within each chain, but antiparallel in adjacent chains. The
result is a peculiar type of frustration of inter-chain interactions, which
leads to an unusual field-temperature phase diagram.
