I consider a brush of gradient polymers, with the chains anchored at their pure A ends with the chemical composition changing linearly along the chain up to the untethered chain tips whose composition is pure B. Demixing of the A and B monomers results in the creation of a thermally-controllable zone from which free ends are excluded. For high temperatures, the zone is small and located near the grafting surface, but for lower temperatures the zone extends throughout the layer, giving a physical manifestation of an Alexander brush. This conclusion is supported by both scaling and numerical self-consistent field calculations. (C) 2003 American Institute of Physics.