We investigate Leifer and Milner \emph{RPO approach} for deriving efficient (finitely branching) LTS's and bisimilarities for $\pi$-calculus. To this aim, we work in a category of \emph{second-order term contexts} and we apply a general \emph{pruning technique}, which allows to simplify the set of transitions in the LTS obtained from the original RPO approach. The resulting LTS and bisimilarity provide an alternative presentation of \emph{symbolic LTS} and Sangiorgi's \emph{open bisimilarity}.
