Reinforcement learning with verifiable rewards (RLVR) offers a verifier-bounded performance ceiling for training multi-turn tool-use agents, yet its trajectory-level credit assignment conflates heterogeneous per-turn outcomes into a single reward signal. On-policy distillation provides dense per-token supervision but is either teacher-bounded or prone to gradient concentration collapse. We introduce $ extbf{CrEST}$, a hierarchical credit assignment framework that retains RL's verifier-bounded ceiling while incorporating dense token-level signals from a privileged self-teacher. $ extbf{CrEST}$ resolves credit at two levels: turn-segmented verified advantages address inter-turn dilution, while entropy-gated self-teacher modulation refines intra-turn token contributions. Experiments on BFCL V3 and WildToolBench show that $ extbf{CrEST}$ consistently outperforms both RL and distillation baselines across two model scales, with the largest gains on long-trajectory and strict session-level metrics. Our work demonstrates that the teacher's role in policy optimization can be reduced from determining update directions to modulating update magnitudes, unlocking dense credit assignment without sacrificing the verifier-bounded ceiling. Blogger's Review: This paper proposes a novel credit assignment framework, $ extbf{CrEST}$, which effectively addresses the credit assignment problem in multi-turn multi-step LLM agents. By retaining the verifier-bounded ceiling of reinforcement learning and incorporating dense token-level signals from a self-teacher, $ extbf{CrEST}$ exhibits superior performance in experiments, particularly on long-trajectory and strict session-level metrics. This achievement provides new insights and methods for training multi-turn multi-step LLM agents, with significant research and application value.