  We discuss the ground state of a pyrochlore lattice of
threefold-orbitally-degenerate $S=1/2$ magnetic ions. We derive an effective
spin-orbital Hamiltonian and show that the orbital degrees of freedom can
modulate the spin exchange, removing the infinite spin-degeneracy
characteristic of pyrochlore structures. The resulting state is a collection of
spin-singlet dimers, with a residual degeneracy due to their relative
orientation. This latter is lifted by a magneto-elastic interaction, induced in
the spin-singlet phase-space, that forces a tetragonal distortion. Such a
theory provides an explanation for the helical spin-singlet pattern observed in
the B-spinel MgTi$_2$O$_4$.
