  We prove a general result on Bailey pairs and show that two Bailey pairs of
Bringmann and Kane are special cases. We also show how to use a change of base
formula to pass from the pairs of Bringmann and Kane to pairs used by Andrews
in his study of Ramanujan's seventh order mock theta functions. We derive
several more Bailey pairs of a similar type and use these to construct a number
of new q-hypergeometric double sums which are mock theta functions. Finally, we
prove identities between some of these mock theta double sums and classical
mock theta functions.
