What is a reasonable approach to prompting when the first response isn't quite right?

Read what came back as evidence about the prompt. A first response that misses usually tells you which part of the request was under-specified: too generic means you set no constraints, off-topic means the goal was never stated, the wrong shape means the format was left open. Change that one thing and ask again.

That is different from sending the identical prompt a second time, which is the move people actually reach for. The same request carries the same information, so you are re-rolling rather than correcting, and any improvement is luck you cannot reproduce.

Anthropic's own advice is to start simple and add complexity only where it is needed, checking each addition to see whether it actually helped. In practice that is two or three rounds: supply the missing constraint, then an example if the shape is still wrong, then split the task if it was doing too much at once.

The useful test on a prompt that keeps failing is whether a colleague with no context could follow it. If they could not, the model cannot either.