  A signed circuit is a minimal signed graph (with respect to inclusion) that
admits a nowhere-zero flow. We show that each flow-admissible signed graph on
$m$ edges can be covered by signed circuits of total length at most
$(3+2/3)\cdot m$, improving a recent result of Cheng et al. [manuscript, 2015].
To obtain this improvement we prove several results on signed circuit covers of
trees of Eulerian graphs, which are connected signed graphs such that removing
all bridges results in a collection of Eulerian graphs.
