  We construct $\alpha$-attractor versions of hybrid inflation models. In these
models, the potential of the inflaton field $\varphi$ is uplifted by the
potential of the second field $\chi$. This uplifting ends due to a tachyonic
instability with respect to the field $\chi$, which appears when $\varphi$
becomes smaller than some critical value $\varphi_{c}$. In the large $N$ limit,
these models have the standard universal $\alpha$-attractor predictions. In
particular, $n_{s }= 1- {2 \over N}$ for the exponential attractors. However,
in some special cases the large $N$ limit is reached only beyond the horizon,
for $N \gtrsim 60$. This may change predictions for the cosmological
observations. For any fixed $N$, in the limit of large uplift $V_{\rm up}$, or
in the limit of large $\varphi_{c}$, we find another attractor prediction, $
n_s = 1$. By changing the parameters $V_{\rm up}$ and $\varphi_{c}$ one can
continuously interpolate between the two attractor predictions $n_{s }= 1- {2
\over N}$ and $n_{s} = 1$. This provides significant flexibility, which can be
very welcome in view of the rapidly growing amount and precision of the
cosmological data. Our main result is not specific to the hybrid inflation
models. Rather, it is generic to any inflationary models where the inflaton
potential, for some reasons, is uplifted, and inflation ends prematurely.
