  In previous works we predicted the existence of a $\bar b \bar b u d$
tetraquark with quantum numbers $I(J^P) = 0(1^+)$ using the static
approximation for the $\bar b$ quarks and neglecting heavy spin effects. Since
the binding energy is of the same order as expected for these heavy spin
effects, it is essential to include them in the computation. Here we present a
corresponding method and show evidence that binding is only slightly weakened
and that the $\bar b \bar b u d$ tetraquark persists.
