  Recently, several proposals have been made to test the quantum superposition
principle in the mesoscopic regime. Most of these tests consist of a careful
measurement of the loss of interference due to decoherence. Here we consider,
instead, the spread in position of a freely falling nanosphere. We study in
depth the dependence of this spread on self-gravity in the presence of
decoherence (exotic and non-exotic). We show that the influence of self-gravity
is robust in the presence of weak decoherence, and quantify this robustness by
introducing a new parameter, the critical decoherence, aimed at estimating the
critical value above which self-gravity is overwhelmed by decoherence. We also
emphasise the crucial role played by the spread of the initial wave packet for
the sensitivity of free-fall experiments to decoherence.
