The bending-induced polarization of barium titanate single crystals has been measured with an aim to elucidate the origin of the large difference between theoretically predicted and experimentally measured flexoelectricity in this material. The results indicate that part of the difference is due to polar regions (short-range order) that exist above T(C) and up to T*≈200-225 °C. Above T*, however, the flexovoltage coefficient still shows an unexpectedly large anisotropy for a cubic material, with (001)-oriented crystals displaying 10 times more flexoelectricity than (111)-oriented crystals. Theoretical analysis shows that this anisotropy cannot be a bulk property, and we therefore interpret it as indirect evidence for the theoretically predicted but experimentally elusive contribution of surface piezoelectricity to macroscopic bending-induced polarization.