  We place observational likelihood constraints on braneworld and
non-commutative inflation for a number of inflaton potentials, using Planck,
WMAP polarization and BAO data. Both braneworld and non-commutative scenarios
of the kind considered here are limited by the most recent data even more
severely than standard general-relativity models. At more than 95 % confidence
level, the monomial potential $V(\phi) \propto \phi^p$ is ruled out for $p \geq
2$ in the Randall--Sundrum (RS) braneworld cosmology and, for $p>0$, also in
the high-curvature limit of the Gauss--Bonnet (GB) braneworld and in the
infrared limit of non-commutative inflation, due to a large scalar spectral
index. Some parameter values for natural inflation, small-varying inflaton
models and Starobinsky inflation are allowed in all scenarios, although some
tuning is required for natural inflation in a non-commutative spacetime.
