Using photoemission electron microscopy combined with x-ray magnetic circular dichroism we show that a progressive spatial confinement of a ferromagnet (FM), either through thickness variation or laterally via patterning, actively controls the domains of uncompensated spins in the antiferromagnet (AF) in exchange-biased systems. Direct observations of the spin structure in both sides of the FM/AF interface in a model system, Ni/FeF2, show that the spin structure is determined by the balance between the competing FM and AF magnetic energies. Coexistence of exchange bias domains, with opposite directions, can be established in Ni/FeF2 bilayers for Ni thicknesses below 10 nm. Patterning the Ni/FeF2 heterostructures with antidots destabilizes the FM state, enhancing the formation of opposite exchange bias domains below a critical antidot separation of the order of a few FeF2 crystal domains. The results suggest that dimensional confinement of the FM may be used to manipulate the AF spin structure in spintronic devices and ultrahigh-density information storage media. The underlying mechanism of the uncompensated AF domain formation in Ni/FeF2 may be generic to other magnetic systems with complex noncollinear FM/AF spin structures.