The endeavor of this work is to study the impact of content popularity in a large-scale Peer-to-Peer network, namely KAD. Armed with the insights gained from an extensive measurement campaign, which pinpoints several deficiencies of the present KAD design in handling popular objects, we set off to design and evaluate an adaptive load balancing mechanism. Our mechanism is backward compatible with KAD, as it only modifies its inner algorithms, and presents several desirable properties: (i) it drives the process that selects the number and location of peers responsible to store references to objects, based on their popularity; (ii) it solves problems related to saturated peers, that entail a significant drop in the diversity of references to objects, and (iii) if coupled with an enhanced content search procedure, it allows a more fair and efficient usage of peer resources, at a reasonable cost. Our evaluation uses a trace-driven simulator that features realistic peer churn and a precise implementation of the inner components of KAD.