  We show that, given a suitable combinatorial specification for a permutation
class $\mathcal{C}$, one can obtain a specification for the juxtaposition (on
either side) of $\mathcal{C}$ with Av(21) or Av(12), and that if the
enumeration for $\mathcal{C}$ is given by a rational or algebraic generating
function, so is the enumeration for the juxtaposition. Furthermore this process
can be iterated, thereby providing an effective method to enumerate any
'skinny' $k\times 1$ grid class in which at most one cell is non-monotone, with
a guarantee on the nature of the enumeration given the nature of the
enumeration of the non-monotone cell.
