  We formulate a theory combining the principles of a scalar-tensor gravity and
the Rastall proposal of a violation of the usual conservation laws. In the
resulting Brans-Dicke-Rastall (BDR) theory the only exact, static, spherically
symmetric solution is a Robinson-Bertotti type solution besides the trivial
Schwarzschild one. The PPN constraints can be completely satisfied for some
values of the free parameters.The cosmological solutions display, among others,
a decelerate-accelerate transition in the matter dominated phase.
