The BICEP2/Keck+PLANCK joint analysis of the 𝐵-model polarization and polarization by foreground dust sets an upper bound on the tensor-to-scalar ratio of 𝑟_0.05 < 0.12 at 95% CL. The popular Starorbinsky model Higgs-inflation or the conformally equivalent Higgs-inflation model allow low 𝑟 values (∼10⁻³). We survey the generalizations of the Starobinsky–Higgs models which would allow larger values (𝑟 ∼ 0.1). The Starobinsky–Higgs inflation models require an exponential potential which can be naturally derived from SUGRA models. We show that a variation of the no-scale SUGRA model can give rise to the generalized Starobinsky models which give large 𝑟. We also examine non-standard boundary conditions which would allow a large deviation of the tensor spectral index from the slow roll values and propose that the presence of a thermal component in the tensor spectrum arises from Gibbons–Hawking temperature of the de-Sitter space.