Today’s technology allows firms to personalise their interaction with consumers to an unprecedented degree, leading to an ever finer-grained segmentation of consumers. Targeted online advertising and online price discrimination are amongst the most salient examples of this development. While personalisation’s effects on consumer welfare are expected to be ambiguous, we identify a particular risk to consumers: being trapped in a ‘targeting pocket’. Constellations are possible in which a market is generally open to competition, but the targeted consumer is only aware of one possible seller. Likewise, a given seller may target individual consumers exclusively with one variant of its product or service. From the perspective of the consumer, such a market could effectively resemble a monopoly without, however, being detected as such by competition-law metrics. We therefore suggest a novel metric with which to measure such concentration as a result of personalisation, 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 to personalised adverts and offers experienced by an average consumer. We demonstrate how CAPI scores allow regulators and auditors to detect potentially harmful targeting pockets which would otherwise remain undiscovered by traditional means of public oversight of adverts. We imagine our index to serve as a monitoring tool which identifies areas of concern in the distribution of personalised offers and services. The CAPI could help to enforce proposed regulation such as, amongst others, the European Union’s Digital Services Act with its advertising repositories and the AI Act with its auditing mandates. We further suggest a novel regulatory response to the risk of consumer harms identified in this paper, the adding of optimised degrees of noise to targeting based on the CAPI. A complete ban of targeted advertising would eliminate all its possible economic benefits to consumers. A partial ban of certain targeting variables as currently envisioned in the Digital Services Act would still allow targeting pockets to occur. We show instead how adding noise via randomly distributed non-personalised adverts can dilute the potential harm of overly concentrated targeting. We further demonstrate how the CAPI can identify the optimal degree of added noise, balancing the protection of consumer choice with the economic interests of advertisers.