Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already cover the safety profile (readOnly, idempotent, non-destructive), and the description goes well beyond them: auth requirement, default/max limit, ordering (updated_at descending), and two concrete error behaviors (HTTP 400 invalid_page_token, inbox_not_found). This is exactly the extra context an agent needs.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Front-loaded with the decision rule, then inputs, then return shape and errors in a logical order. The run-on enumeration of thread fields is dense but earns its place since there is no output schema; it could be trimmed slightly.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With no output schema, the description fully compensates by spelling out the return envelope (object/data/next_page_token), per-thread fields, ordering, and error cases. Nothing an agent needs to call and consume this tool correctly is missing.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%, so the schema already documents all five parameters, including the inbox_id omission semantics and the page_token failure mode. The description largely restates these, adding only minor framing ('cursor from a previous page'), so baseline 3 is appropriate.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific resource (threads) with a clear scoping rule — 'whole conversations instead of individual messages' — which cleanly separates it from cooper_list_messages and cooper_search_messages in the sibling set. The enumerated thread fields confirm exactly what a 'thread' means here.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Gives an explicit when-to-use with a concrete example ('see who is in a thread and when the last reply arrived') and contrasts it with message-level retrieval. It does not name the alternative tool by name (e.g. cooper_list_messages / cooper_search_threads), so the routing is implied rather than explicit.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.