Most popular OSNs currently restrict the number of social links that a user can have, in order to deal with the problems of increasing spam and scalability in the face of a rapid rise in the number of users in recent years. However such restrictions are often being criticized by socially active and popular users, hence the OSN authorities are facing serious design-choices while imposing restrictions; this is evident from the innovative ‘soft’ cut-off recently imposed in Twitter instead of the traditional ‘hard’ cut-offs in other OSNs. Our goal in this paper is to develop an analytical framework taking the restriction in Twitter as a case-study, that can be used to make proper design-choices considering the conflicting objectives of reducing system-load and minimizing user-dissatisfaction. We consequently define a simple utility function considering the above two objectives, and find that Twitter’s policy well balances both. From a network science perspective, this is the first analysis of ‘soft’ cut-offs in any sort of network, to the best of our knowledge.