  We consider the fundamental Matroid Theory problem of finding a circuit in a
matroid spanning a set T of given terminal elements. For graphic matroids this
corresponds to the problem of finding a simple cycle passing through a set of
given terminal edges in a graph. The algorithmic study of the problem on
regular matroids, a superclass of graphic matroids, was initiated by
Gaven\v{c}iak, Kr\'al', and Oum [ICALP'12], who proved that the case of the
problem with |T|=2 is fixed-parameter tractable (FPT) when parameterized by the
length of the circuit. We extend the result of Gaven\v{c}iak, Kr\'al', and Oum
by showing that for regular matroids
  - the Minimum Spanning Circuit problem, deciding whether there is a circuit
with at most \ell elements containing T, is FPT parameterized by k=\ell-|T|;
  - the Spanning Circuit problem, deciding whether there is a circuit
containing T, is FPT parameterized by |T|. We note that extending our
algorithmic findings to binary matroids, a superclass of regular matroids, is
highly unlikely: Minimum Spanning Circuit parameterized by \ell is W[1]-hard on
binary matroids even when |T|=1. We also show a limit to how far our results
can be strengthened by considering a smaller parameter. More precisely, we
prove that Minimum Spanning Circuit parameterized by |T| is W[1]-hard even on
cographic matroids, a proper subclass of regular matroids.
