A Sybil attack is one of the main challenges to be addressed when securing peer-to-peer networks, especially those based on Distributed Hash Tables (DHTs). Tampering routing tables by means of multiple fake identities can make routing, storing, and retrieving operations significantly more difficult and time-consuming. Countermeasures based on trust and reputation have already proven to be effective in some contexts, but one variant of the Sybil attack, the Spartacus attack, is emerging as a new threat and its effects are even riskier and more difficult to stymie. In this paper, we first improve a well-known and deployed DHT (Chord) through a solution mixing trust with standard operations, for facing a Sybil attack affecting either routing or storage and retrieval operations. This is done by maintaining the least possible overhead for peers. Moreover, we extend the solution we propose in order for it to be resilient also against a Spartacus attack, both for an iterative and for a recursive lookup procedure. Finally, we validate our findings by showing that the proposed techniques outperform other trust-based solutions already known in the literature as well.