Existing LLM data-analyst benchmarks fix data access at full disclosure and evaluate only on answer accuracy. But real deployments rarely grant full access. No prior work, to our knowledge, asks *"what’s the least amount of information needed for the agent to work?"*. In this article, we treat dataset disclosure as a controlled treatment along a *graduated information-disclosure* (GID) axis: C₀ (column names) and C∞ (full table) bracket a nested chain C₁ ⊆ … ⊆ C₅ that adds per-column metadata, dataset purpose, summary statistics, sampled cells, and sampled rows. We maintain agent architecture, tool registry, and decoding fixed, and score the final reports on a 14-attribute rubric across a 6 × 4 × 12 panel of frontier models, planted-signal datasets, and disclosure levels. At a high level, from C₀ to C∞, seven attributes rise and five fall. However, the rise/fall pattern has nuance, the optimal intermediate level depends on several factors including models, datasets and attributes. Level C₁ - one sentence of types and units beyond column names - matches (statistically) C∞ on signal recovery and decoy rejection at ∼49× lower prompt-token cost. The key takeaway from this work is - **current LLM data-science agents can act on partial information alone**, so row-level records need never leave the institution. Hence, the current framework also offers a way to enforce data boundary constraints (required by GDPR) without compromising on quality.