A method for producing a heterologous non-catabolic compound in a genetically modified yeast host cell, the method comprising: (a) culturing a population of genetically modified yeast host cells in a culture medium comprising a carbon source comprising maltose, wherein the host cell comprises one or more heterologous nucleic acids encoding one or more enzymes of an enzymatic pathway for making the heterologous non-catabolic compound, wherein expression of the one or more enzymes is negatively regulated by the activity of a maltose-responsive promoter, wherein the presence of maltose in the culture medium limits the amount of heterologous non-catabolic compound produced by the host cells; (b) culturing said population or a subpopulation thereof in a culture medium comprising a carbon source wherein maltose is absent or in sufficiently low amounts such that the maltose-responsive promoter is no longer active, and production of the heterologous non-catabolic compound by the host cells is increased; and (c) optionally recovering the non-catabolic compound, wherein: (i) the maltose-responsive promoter is operably linked to a heterologous nucleic acid encoding a GAL80 gene product; (ii) the host cell comprises Gal4p; and (iii) the one or more enzymes of the enzymatic pathway are each operably linked to a Gal4p-responsive promoter; wherein the maltose in step (a) increases the expression of the GAL80 gene product and negatively regulates the expression of the one or more heterologous nucleic acids encoding the one or more enzymes of the enzymatic pathway. (a) culturing a population of genetically modified yeast host cells in a culture medium comprising a carbon source comprising maltose, wherein the host cell comprises one or more heterologous nucleic acids encoding one or more enzymes of an enzymatic pathway for making the heterologous non-catabolic compound, wherein expression of the one or more enzymes is negatively regulated by the activity of a maltose-responsive promoter, wherein the presence of maltose in the culture medium limits the amount of heterologous non-catabolic compound produced by the host cells; (b) culturing said population or a subpopulation thereof in a culture medium comprising a carbon source wherein maltose is absent or in sufficiently low amounts such that the maltose-responsive promoter is no longer active, and production of the heterologous non-catabolic compound by the host cells is increased; and (c) optionally recovering the non-catabolic compound, wherein: (i) the maltose-responsive promoter is operably linked to a heterologous nucleic acid encoding a GAL80 gene product; (ii) the host cell comprises Gal4p; and (iii) the one or more enzymes of the enzymatic pathway are each operably linked to a Gal4p-responsive promoter; wherein the maltose in step (a) increases the expression of the GAL80 gene product and negatively regulates the expression of the one or more heterologous nucleic acids encoding the one or more enzymes of the enzymatic pathway. (i) the maltose-responsive promoter is operably linked to a heterologous nucleic acid encoding a GAL80 gene product; (ii) the host cell comprises Gal4p; and (iii) the one or more enzymes of the enzymatic pathway are each operably linked to a Gal4p-responsive promoter;