  This paper examines a class of singular stochastic control problems with
convex objective functions. In Section 2, we use tools from convex analysis to
derive necessary and sufficient first order conditions for this class of
optimisation problems. The main result of this paper is Theorem 9 which uses
results from optimal stopping to establish the link between singular stochastic
control and Gittin's index without the need to appeal to the representation
result in [5]. In Sections 3-5 we assume the singular control problem is driven
by a L\'{e}vy process. Expressions for the Gittin's index are derived in terms
of the Wiener-Hopf factorisation. This allows us to broaden the class of
parameterised optimal stopping problems with explicit solutions examined in [6]
and derive explicit solutions to the singular control problems studied in
Section 2. In Section 4, we apply our results to the `monotone follower'
problem which originates in [7] and [28]. In Section 5, we apply our results to
an irreversible investment problem which has been studied in [9], [35] and
[40].
