  In this paper, we study the tedious link between the properties of
sensibility and approximability of models of untyped {\lambda}-calculus.
Approximability is known to be a slightly, but strictly stronger property that
sensibility. However, we will see that so far, each and every (filter) model
that have been proven sensible are in fact approximable. We explain this result
as a weakness of the sole known approach of sensibility: the Tait reducibility
candidates and its realizability variants. In fact, we will reduce the
approximability of a filter model D for the {\lambda}-calculus to the
sensibility of D but for an extension of the {\lambda}-calculus that we call
{\lambda}-calculus with D-tests. Then we show that traditional proofs of
sensibility of D for the {\lambda}-calculus are smoothly extendable for this
{\lambda}-calculus with D-tests.
