An arbitration mechanism for balancing memory requests issued by parallel texture pipelines in a multiple pipeline texture engine. The mechanism ensures that, as polygon textures are processed by a texture engine, all of the memory requests associated with a portion of a given graphics texture are issued by all texture pipelines before any texture pipeline may issue a memory request for another portion of a graphics texture. Thus, the invention balances graphics texture processing between parallel texture pipelines operating together, thereby improving processing efficiency and preventing deadlock conditions.