Solvers in the framework of Satisfiability Modulo Theories (SMT) have been widely successful in practice. Recently there has been an increasing interest in solvers for string constraints to address security issues in web programming, for example. To be practically useful, the solvers need to support an expressive constraint language over unbounded strings, and in particular, over string lengths. Satisfiability checking for these formulas, especially in the SMT context, is very hard; it is generally undecidable for a rich fragment. In this paper, we propose a form of dependency analysis for a rich fragment of string constraints including high-level operations such as length, contains to deal with their inter-theory interaction so as to solve them more efficiently. We implement our dependency analysis in the string theory of the Z3 solver to obtain a new one, called S3N. Finally, we demonstrate the superior performance of S3N over state-of-the-art string solvers such as Z3str3, CVC4, S3P, and Z3 on several large industrial-strength benchmarks.