  We consider the Bouchaud trap model on the integers in the case that the trap
distribution has a slowly varying tail at infinity. We prove that the model
eventually localises on exactly two sites with overwhelming probability. This
is a stronger form of localisation than has previously been established in the
literature for the Bouchaud trap model on the integers in the case of regularly
varying traps. Underlying this result is the fact that the sum of a sequence of
i.i.d. random variables with a slowly varying tail is asymptotically dominated
by the maximal term.
