SMT-based program verification can achieve high precision using bit-precise models or combinations of different theories. Often such approaches suffer from problems related to scalability due to the complexity of the underlying decision procedures. Precision is traded for performance by increasing the abstraction level of the model. As the level of abstraction increases, missing important details of the program model becomes problematic. In this paper we address this problem with an incremental verification approach that alternates precision of the program modules on demand. The idea is to model a program using the lightest possible (i.e., less expensive) theories that suffice to verify the desired property. To this end, we employ safe over-approximations for the program based on both function summaries and light-weight SMT theories. If during verification it turns out that the precision is too low, our approach lazily strengthens all affected summaries or the theory through an iterative refinement procedure. In order to connect different theories, we design a flexible function summarization framework that avoids the need for prohibitively complicated and expensive theory combination. An experimental evaluation with a bounded model checker for C on a wide range of benchmarks demonstrates that our approach scales well, often effortlessly solving instances where the state-of-the-art model checker CBMC runs out of time or memory.