  Careful numerical computations show that very slight geometrical
imperfections of the cross-section of actual large air-fraction holey fibres
(d/{\Lambda} > 0.6) may induce surprisingly high birefringence, corresponding
to beat lengths as short as few millimeters. The spectral variations of this
birefringence obeys laws similar to those of elliptical core Hi-Bi holey fibres
with low air-fraction. For all the tested fibres, the group birefringence
numerically deduced from the only shape birefringence is in good agreement with
the measured one that does not varies when strongly heating the fibres. These
computations and measurements show that the contribution of possible inner
stress to the birefringence is negligible.
