How cells choose between carbon sources is a classic example of cellular decision-making. Microbes often prioritise glucose, but there has been little investigation of whether other sugars are also preferred. Here we study budding yeast growing on mixtures of sugars with palatinose, a sucrose isomer that cells catabolise with the MAL regulon. We find that the decision-making involves more than carbon flux-sensing: yeast prioritise galactose over palatinose, but sucrose and fructose weakly if at all despite each allowing faster growth than palatinose. With genetic perturbations and transcriptomics, we show that the regulation is active with repression of the MAL genes via Gal4, the GAL regulon's master regulator. We argue, using mathematical modelling, that cells enforce their preference for galactose through weakening the MAL regulon's positive feedback. They do so through decreasing intracellular palatinose by repressing MAL11, the palatinose transporter, and expressing the isomaltases IMA1 and IMA5. Supporting these predictions, we show that deleting IMA1 abolishes diauxie. Our results demonstrate that budding yeast actively prioritises carbon sources other than glucose and that such priorities need not reflect differences in growth rates. They imply that carbon-sensing strategies even in model organisms are more complex than previously thought.