Disclosed herein are materials and methods for creating and/or isolating variants of yeasts especially variants of Saccharomyces cerevisiae that can grow on sugars other than D-glucose in the presence of amounts of 2-deoxy-glucose and or D-glucose that inhibit most strains of yeast from growing on sugars other than D-glucose. Selection media that can be used to isolate such variants include pentose sugars such as D-xylose, L-glutamine and 2-deoxy-glucose. Mutations in the Grr1 and Red genes in some strains also produce variants that can grow on sugars including the pentose D-xylose in the presence of 2-deoxy-glucose.