  We consider the quenched localisation of the Bouchaud trap model on the
positive integers in the case that the trap distribution has a slowly varying
tail at infinity. Our main result is that for each $N \in \{2, 3, \ldots\}$
there exists a slowly varying tail such that quenched localisation occurs on
exactly $N$ sites. As far as we are aware, this is the first example of a model
in which the exact number of localisation sites are able to be `tuned'
according to the model parameters. Key intuition for this result is provided by
an observation about the sum-max ratio for sequences of independent and
identically distributed random variables with a slowly varying distributional
tail, which is of independent interest.
