  By writing the running of the scalar spectral index completely in terms of
the scalar index $n_s$ and the tensor-to-scalar ratio $r$ we are able to impose
constraints to models of inflation which are independent of the parameters of
the model in question. We write analytical expressions for the running index of
Natural Inflation, two models of the type Mutated Hilltop Inflation and the
Starobinsky model. The resulting formulae for the running depend exclusively on
$n_s$ and/or $r$ and will keep tightening the running index further as
additional conditions and observations constrain the scalar and the
tensor-to-scalar indices.
