Structural distortions in cuprate materials give a natural origin for aniso
tropies in electron properties. We study a modified one-band t-J model in w
hich we allow for different hoppings and antiferromagnetic couplings in the
two spatial directions (t(x) not equal t(y) and J(x) not equal J(y)). Inco
mmensurate peaks in the spin structure factor show up only in the presence
of a lattice anisotropy, whereas charge correlations, indicating enhanced f
luctuations at incommensurate wave vectors, are present but almost unaffect
ed with respect to the isotropic case.