Cosmological α-attractors are a compelling class of inflationary models. They lead
to universal predictions for large-scale observables, broadly independent from the functional form
of the inflaton potential. In this work we derive improved analytical predictions for the
large-scale observables, whose dependence on the duration of reheating and the parameter α
is made explicit. We compare these with Planck and BICEP/Keck 2018 data in the framework
of a Bayesian study, employing uniform logarithmic and linear priors for α. Our improved
universal predictions allow direct constraints on the duration of reheating. Furthermore, while it
is well-known that CMB constraints on the tensor-to-scalar ratio can be used to place an upper
bound on the α parameter, we demonstrate that including the α-dependence of the
scalar spectral tilt yields novel constraints on α. In particular, for small α, the
scalar spectral tilt scales with log10
α, regardless of the specific potential
shape. For decreasing α, this eventually puts the models in tension with CMB measurements,
bounding the magnitude of α from below. Therefore, in addition to the upper bound from the
tensor-to-scalar ratio, we derive the first lower bound on the magnitude of α for
α-attractor T-models, log10
α = -4.2+5.4
-8.6 at 95% C.L.