Firms are increasingly personalising their offers and services, leading to an ever finer-grained segmentation of consumers online. Targeted online advertising and online price discrimination are salient examples of this development. While personalisation's overall effects on consumer welfare are expectably ambiguous, it can lead to concentration in the distribution of advertising and commercial offers. Constellations are possible in which a market is generally open to competition, but the targeted consumer is only made aware of one possible seller. For the consumer, such a market could effectively resemble a monopoly. We call such extreme cases ‘targeting pockets’. Competition-law metrics such as the Herfindahl–Hirschman Index and traditional means of public oversight of adverts would not detect this concentration. We, therefore, suggest a novel metric, the Concentration-after-Personalisation Index (CAPI). The CAPI treats every consumer as a separate ‘market’, computes a measure of concentration for personalised adverts and offers for each individual consumer separately, and then averages the result to measure the exposure experienced by an average consumer. We demonstrate how the CAPI can serve as a monitoring tool for regulators and auditors and thus help to enforce existing consumer law as well as proposed new regulations such as the European Union's Digital Services Act and its Artificial Intelligence Act. We further show how adding noise via randomly distributed non-personalised adverts can dilute the potential harm of overly concentrated personalisation. We demonstrate how the CAPI can identify the optimal degree of added noise, balancing the protection of consumer choice with the economic interests of advertisers.