  We discuss the errors introduced by level truncation in the study of boundary
renormalisation group flows by the Truncated Conformal Space Approach. We show
that the TCSA results can have the qualitative form of a sequence of RG flows
between different conformal boundary conditions. In the case of a perturbation
by the field phi(13), we propose a renormalisation group equation for the
coupling constant which predicts a fixed point at a finite value of the TCSA
coupling constant and we compare the predictions with data obtained using TBA
equations.
