The positive BOLD (blood oxygen level-dependent) response elicited in human visual cortex by a localized visual stimulus is accompanied by a reduction in the BOLD response in regions of the visual cortex that represent unstimulated locations in the visual field. We have suggested previously that this negative BOLD reflects attention-related suppression of neural activity, but it might also be explained in terms of "blood stealing," i.e., hemodynamic changes that have no neural correlate. We distinguish two possible hemodynamic effects of this type: (1). blood flow reduction caused by locally reduced pressure in vessels that share their blood supply with nearby dilated vessels; and (2). blood flow reduction caused by active constriction of vessels under neural control. The first is ruled out as an explanation of negative BOLD by showing that a visual stimulus that stimulates primary visual cortex in one hemisphere can cause extensive suppression in the other hemisphere i.e., it is not a local phenomenon. Negative BOLD most likely reflects suppression of neural activity, but could also reflect an active blood flow control system.