YBa2Cu3-xAlxO6+delta single crystals with different Al contents (x = 0.06, 0.14 and 0.19) were heat treated in different atmospheres, The oxidized as-grown crystals show a macroscopically tetragonal tweed-structure. The oxygen content delta in the Cu(1) layer of these oxidized samples is significantly lower than 1, which results from the Al coordination disturbing the ordering in the chain-oxygen sublattice. Neutron-diffraction data show that upon reduction at 1044 K the oxygen content delta within the Cu(1) layer remains at 0.25 due to pinning of excess oxygen by the aluminum at x = 0.19. Crystals annealed in reducing atmospheres at temperatures above 973 K develop orthorhombic long-range order after reoxidation at 673 K, probably due to short-range clustering of the AlOn defects. The obtained orthorhombicity of the reoxidized material decreases with decreasing temperature of the reduction treatment, No change in the structural state is obtained when the reducing treatment is performed below 950 K; the reoxidized samples remain macroscopically tetragonal. Annealing the samples at 1073 K in oxygen restores the tweed structure. An evolution of the tweed structure with annealing time towards orthorhombic long-range order was not observed.