Ephemeral Diffie-Hellman Over COSE (EDHOC) aims at being a very compact and lightweight authenticated Diffie-Hellman key exchange with ephemeral keys. It is expected to provide mutual authentication, forward secrecy, and identity protection, with a 128-bit security level.A formal analysis has already been proposed at SECRYPT ’21, on a former version, leading to some improvements, in the ongoing evaluation process by IETF. Unfortunately, while formal analysis can detect some vulnerabilities in the protocol, it cannot evaluate the actual security level.In this paper, we study the protocol as it appeared in version 15. Without complete breaks, we anyway exhibit attacks in 2^64 operations, which contradict the expected 128-bit security level. We thereafter propose improvements, some of them being at no additional cost, to achieve 128-bit security for all the security properties (i.e. key privacy, mutual authentication, and identity-protection).