In this paper we investigate fair computations in the $\pi$-calculus \cite{MPW92}. Following Costa and Stirling's approach for CCS-like languages \cite{CS84,CS87}, we consider a method to label process actions in order to filter out unfair computations. We contrast the existing fair-testing notion \cite{RV07,NC95} with those that naturally arise by imposing weak and strong fairness. This comparison provides insight about the expressiveness of the various `fair' testing semantics and about their discriminating power.