Strong dot-size dependence of the positive exchange bias onset with the cooling field was found in Ni/FeF2 exchange biased nanostructures. With increasing cooling field, the sign of the exchange bias field changes from negative to coexistence of positive and negative, and eventually to positive. As the structure size decreases, the lower limit of cooling fields necessary for only positive exchange bias also decreases and is one order of magnitude smaller than that of unpatterned films. This behavior is attributed to comparable Ni dot size with the antiferromagnet “domain” size estimated to be about 500 nm.