  Two questions that naturally arise in N-body simulations of stellar systems
are: (1) How can we compare experiments that employ different types of softened
gravity? (2) Given a particular type of softened gravity, which choices of the
softening length optimize the faithfulness of the experiments to the Newtonian
dynamics? We devise a method for exploring the dynamical effects of softening,
which provides detailed answers in the case of 2-D simulations of disc galaxies
and also solves important aspects of the 3-D problem. In the present paper we
focus on two applications that reveal the dynamical differences between the
most representative types of softened gravity, including certain anisotropic
alternatives. Our method is potentially important not only for testing but also
for developing new ideas about softening. Indeed, it opens a direct route to
the discovery of optimal types of softened gravity for given dynamical
requirements, and thus to the accomplishment of a physically consistent
modelling.
