  F\"uhrmann introduced Abstract Kleisli structures to model call-by-value
programming languages with side effects, and showed that they correspond to
monads satisfying a certain equalising condition on the unit. We first extend
this theory to non-strict morphisms of monads, and to incorporate $2$-cells of
monads. We then further extend this to a theory of abstract Kleisli structures
on $2$-categories, characterising when the original pseudomonad can be
recovered by the abstract Kleisli structure on its $2$-category of
free-pseudoalgebras.
