In UMTS mobile networks, there are some circumstances that the International Mobile Subscriber Identity (IMSI) of a user is conveyed in clear-text over the radio interface. Such situations violate the anonymity of users. In this paper, we introduce an Improved User Identity Confidentiality (IUIC) mechanism which attempts to avoid the drawback and makes users more anonymous. We give the role of IMSI to anonymous tickets in such a way that IMSI is never exposed on the radio interface or over any other link. Our IUIC mechanism employs symmetric cryptography based on the existing network access security features of UMTS. Its implementation, security, and performance issues are also considered.