  Finite-size corrections to scaling of critical correlation lengths and free
energies of Ising and three-state Potts ferromagnets are analysed by numerical
methods, on strips of width $N$ sites of square, triangular and honeycomb
lattices. Strong evidence is given that the amplitudes of the ``analytical''
correction terms, $N^{-2}$, are identically zero for triangular-- and honeycomb
Ising systems. For Potts spins, our results are broadly consistent with this
lattice-dependent pattern of cancellations, though for correlation lengths
non-vanishing (albeit rather small) amplitudes cannot be entirely ruled out.
