The Natural Monopoly is a robust empirical generalisation that describes the tendency for more popular brands to attract light users of the product category. This study shows that this pattern can also explain the underlying ‘trade-off’ between associations that consumers hold in memory for a specific brand vs. other brands, given the same range of category cues or category entry points (e.g., purchase or consumption situations, core benefits etc.). Specifically, the Natural Monopoly can be extended to explain that consumers with limited knowledge of brands are more likely to memorise associations primarily in relation to the most popular brands of the category, which ‘monopolise’ category entry points. This is confirmed with broadly consistent results across three data sets, multiple time-periods and a total of six categories (including CPGs, services and mobile applications). As such, this study significantly expands the generalisability of the Natural Monopoly empirical law by showcasing it as a ‘tool’ to extend knowledge on brand image associations. The results also yield important practical implications for growing a brand's mental availability. For the most popular brands, the outcomes of this study highlight the relevance of reaching out to consumers with limited knowledge of brands within the same category; for the least popular brands, they indicate the importance of building associations with category entry points.