  A new flavour of amenability for discrete semigroups is proposed that
generalises group amenability and follows from a \Folner-type condition. Some
examples are explored, to argue that this new notion better captures some
essential ideas of amenability. A semigroup $S$ is left fairly amenable if, and
only if, it supports a mean $m\in\ell^\infty(S)^*$ satisfying $m(f) = m(s\ast
f)$ whenever $s\ast f\in\ell^\infty(S)$, thus justifying the nomenclature
"fairly amenable''.
