Cloud storage systems showcase a range of consistency models, from weak to strong consistency. Weakly consistent systems enable better performance, but cannot maintain strong application invariants, which strong consistency trivially supports. This paper takes the position that it is possible to both achieve fast operation and maintain application invariants. To that end, we propose the novel abstraction of invariant-preserving CRDTs, which are replicated objects that provide invariant-safe automatic merging of concurrent updates. The key technique behind the implementation of these CRDTs is to move replica coordination outside the critical path of operations execution, to enable low normal case latency while retaining the coordination necessary to enforce invariants. In this paper we present ongoing work, where we show different invariant-preserving CRDTs designs and evaluate the latency of operations using a counter that never goes negative.