  We present a new method to observe direct experimental evidence of
Jaynes--Cummings nonlinearities in a strongly dissipative cavity quantum
electrodynamics system, where large losses compete with the strong light-matter
interaction. This is a highly topical problem, particularly for quantum dots in
microcavities where transitions from higher rungs of the Jaynes--Cummings
ladder remain to be evidenced explicitly. We compare coherent and incoherent
excitations of the system and find that resonant excitation of the detuned
emitter make it possible to unambiguously evidence few photon quantum
nonlinearities in currently available experimental systems.
