  We study the structure of infinite discrete sets D definable in expansions of
ordered Abelian groups whose theories are strong and definably complete, with
particular emphasis on the set D' comprised of differences between successive
elements. In particular, if the burden of the structure is at most n, then the
result of applying the operation taking D to D' n times must be a finite set
(Theorem 1.1). In the case when the structure is densely ordered and has burden
2, we show that any definable unary discrete set must be definable in some
elementary extension of the structure (R; <, +, Z) (Theorem 1.3).
