  In this paper we study a simple example of a two-parameter space of
renormalisation group flows of defects in Virasoro minimal models. We use a
combination of exact results, perturbation theory and the truncated conformal
space approach to search for fixed points and investigate their nature. For the
Ising model, we confirm the recent results of Fendley et al. In the case of
central charge close to one, we find six fixed points, five of which we can
identify in terms of known defects and one of which we conjecture is a new
non-trivial conformal defect. We also include several new results on exact
properties of perturbed defects and on the renormalisation group in the
truncated conformal space approach.
