  We present new examples of deformations of smash product algebras that arise
from Hopf algebra actions on pairs of module algebras. These examples involve
module algebras that are Koszul, in which case a PBW theorem we established
previously applies. Our construction generalizes several `double' constructions
appearing in the literature, including Weyl algebras and some types of
Cherednik algebras, and it complements the braided double construction of
Bazlov and Berenstein. Many suggestions of further directions are provided at
the end of the work.
