  In the real-analytic setting, we show that all sub-Riemannian minimizers
(parametrized by the arc-length) are real-analytic everywhere except an at most
countable non-dense set. In particular, non-analyticity may occur only on a set
of measure zero of the domain of definition of a sub-Riemannian minimizer.
Furthermore, we provide a geometrical condition which implies the absence of
the so called strictly abnormal minimizers. In particular, under such
condition, all sub-Riemannian minimizers (parametrized by the arc-length) are
real-analytic.
