This study investigates if and how the translation of different types of functionality into measurable “amounts” of healthiness influences parents' preference for an a priori unhealthy (but tasty) food product (i.e., sweet or salty children's snacks). Moreover, it aims to explore whether perceptions about healthiness related to functionality types differ among consumers according to their level of prior awareness of functionality and its health benefits. The application of the discrete choice experimental technique on a sample of 140 parents with at least one 5- to 14-year-old child was selected as the most suitable methodological approach. The sample purposively comprised two subsamples of 70 parents each, based on their real awareness of the term “functional” and of the health benefits of specific functionality types. Parents generally perceived functionality as a product attribute that contributes positively to the image enhancement of the (unhealthy) target product and affirmed that they are willing to pay reasonable premiums for it. However, the level of consumers' prior awareness of functionality played a decisive role in their preference for functional products. The type of food that “carries” functionality was also more important when consumers had no knowledge of functionality. Overall, prior and accurate awareness was found to increase the variety of functionality types and preferred carriers, the strength of preference per functionality type, and the price premiums willingly paid.