  Using a self-consistent Hartree-Fock approximation we investigate the
relative stability of various stripe phases in the extended $t$-$t'$-$U$
Hubbard model. One finds that a negative ratio of next- to nearest-neighbor
hopping $t'/t<0$ expells holes from antiferromagnetic domains and reinforces
the stripe order. Therefore the half-filled stripes not only accommodate holes
but also redistribute them so that the kinetic energy is gained, and these
stripes take over in the regime of $t'/t\simeq -0.3$ appropriate for
YBa$_2$Cu$_3$O$_{6+\delta}$.
