Developing multi-turn interactive tool-use agents is challenging because real-world user needs are often complex and ambiguous, yet agents must execute deterministic actions to satisfy them. To address this gap, we introduce \textbf{CoVe} (\textbf{Co}nstraint-\textbf{Ve}rification), a post-training data synthesis framework designed for training interactive tool-use agents while ensuring both data complexity and correctness. CoVe begins by defining explicit task constraints, which serve a dual role: they guide the generation of complex trajectories and act as deterministic verifiers for assessing trajectory quality. This enables the creation of high-quality training trajectories for supervised fine-tuning (SFT) and the derivation of accurate reward signals for reinforcement learning (RL). Our evaluation on the challenging $τ^2$-bench benchmark demonstrates the effectiveness of the framework. Notably, our compact \textbf{CoVe-4B} model achieves success rates of 43.0\% and 59.4\% in the Airline and Retail domains, respectively; its overall performance significantly outperforms strong baselines of similar scale and remains competitive with models up to $17\times$ its size. These results indicate that CoVe provides an effective and efficient pathway for synthesizing training data for state-of-the-art interactive tool-use agents. To support future research, we open-source our code, trained model, and the full set of 12K high-quality trajectories used for training.