Perceptual learning involves modification of cortical processes so that transfer to new task variants depends on neuronal representation overlap. Neuron selectivity varies with cortical level, so that the degree of transfer should depend on training-induced modification level. We ask how different can stimuli be, how far apart can their representations be, and still induce training transfer. We measure transfer across both long distances within the visual field, namely across cerebral hemispheres, as well as across perceptual dimensions, i.e., between detection of odd color and orientation. In Experiment 1, subjects learned feature search using eccentric arrays randomly presented in the right or left hemifield. Odd elements differed in color or orientation, depending on the presentation hemifield. Following training and performance improvement, the dimensions were switched between hemifields. There was little cross-hemifield or cross-task transfer for difficult cases, and the greater transfer found for easier cases could be across hemispheres and/or perceptual dimensions. Testing these two elements separately, Experiment 2 confirmed considerable transfer across task dimensions, training one dimension and testing another, and Experiment 3 confirmed such transfer across hemifields, training search on one side and testing on the other. Results support Reverse Hierarchy Theory (M. Ahissar & S. Hochstein, 1997, 2004) in that, for easier perceptual tasks involving and modifying higher cortical levels, considerable transfer occurs both across perceptual dimensions and across visual field location even across hemifields.