  The $R+R^2$ model is successful in describing inflation, as it provides an
excellent fit to the full set of available observational data. On the other
hand, the same model is the simplest extension of general relativity which does
not produce higher derivative ghosts and related instabilities. Long ago, it
was proposed to treat all terms which cause higher derivative instabilities as
small perturbations that could avoid the presence of ghosts in the spectrum. We
put this proposal into practice and consider an explicit example of treating
more complicated higher derivative terms as small perturbations over the
$R+R^2$ model by introducing the $R\Box R$ term into the action. Within the
described scheme, it is possible to obtain an upper bound on the coefficient of
this non-scale-free sixth-derivative term by mapping the theory into a
one-scalar field potential. It is shown that the result differs from treating
this term on equal footing with other terms that requires mapping to a
two-scalar field model, and in general leads to different observational
consequences.
