When a ferromagnet is in proximity with an antiferromagnet, lateral length scales such as the respective magnetic domain sizes drastically affect the exchange bias. Bilayers of FeF2 and either Ni, Co or Fe are studied using SQUID and spatially resolved MOKE. When the antiferromagnetic domains are larger than or comparable to the ferromagnetic domains, a local, non-averaging exchange bias is observed. This gives rise to unusual and tunable magnetic hysteresis curves. ; Comment: 14 pages, 2 in-line figures. Submitted to PRL