I will discuss a curious approach to the Kirby calculus discovered in an unsuccessful attempt to find a combinatorially defined invariant of smooth 4-manifolds: by using framed string links, rather than links, it is possible to 'package' the band-sum moves which encode handle-slides, and the 'missing isotopies' to pass from the theory of framed string links to framed links into an action of an extension of Gl(n,Z) on n-component string links.