Linearizability, the de facto correctness condition for concurrent data structure implementations, despite its intuitive appeal is known to lead to poor scalability. This disadvantage has led researchers to design scalable data structures satisfying consistency conditions weaker than linearizability. Despite this recent trend, sequential consistency as a strictly weaker consistency condition than linearizability has received no interest. In this paper, we investigate the applicability of sequential consistency as an alternative correctness criterion for concurrent data structure implementations. Our first finding formally justifies the reluctance in moving towards sequentially consistent data structures: Implementations in which each thread modifies only its thread-local variables are sequentially consistent for various standard data structures such as pools, queues and stacks. We also show that for almost all data structures, and the data structures we consider in this paper, it is possible to have sequentially consistent behaviors in which a designated thread does not synchronize at all. As a potential remedy, we define a hierarchy of quantitatively strengthened variants of sequential consistency such that the stronger the variant the more synchronization it enforces which at the limit is equal to that enforced by linearizability.