The generalized bracket framework is used to derive a family of compressible viscoelastic models. The framework accounts for both reversible and non-reversible dynamics and ensures that the derived models are consistent with the laws of thermodynamics. The most general compressible forms of the UCM and Oldroyd B models are derived. For these models the elastic strain energy is taken to be that for a Hookean material. Nonlinear elastic strain energy functionals are also considered and used to derive new viscoelastic models. The viscometric behaviour of these models is investigated and model predictions are compared with experimental data for Boger fluids and mLLDPE.