In this talk, I will discuss the optimal control problem for a control-affine system, where the L^1 norm of the control is minimized. First, I will show how Pontryagin Maximum Principle applies to this problem and divide the extremal trajectories into two categories: regular and singular extremals. Then, I will show that a strong generalized Legendre-Clebsch condition (SGLC) for singular extremals allows to build an overmaximized Hamiltonian function, which can be used to prove optimality of short singular arcs. Moreover, SGLC together with the absence of conjugate points is sufficient to ensure local strong optimality of a singular extremal. Finally, I will discuss an example of left-invariant control system on the Lie group SU(2) where our results can be applied.