  Recently, a class of spherically symmetric thin-shell wormholes in
Brans-Dicke gravity have been introduced. Such wormholes can be supported by
matter satisfying the weak energy condition (WEC). In this paper, we first
obtain all the exact solutions satisfying the WEC. Then we show these solutions
can be stable for certain parameters. A general requirement for stability is
that $\beta^2>1$, which may imply that the speed of sound exceeds the speed of
light.
