The prompt you ship is never one instruction. It asks for JSON so your parser can read it, it opens with a persona because someone found that helped, and it says the request is urgent because the endpoint is on an incident path. Each of those, benchmarked on its own, is harmless — a point or two either way. Run all 27 combinations of format, persona and urgency across 164 coding problems and five models, 22,140 graded runs, and the combinations do something the single-factor tests cannot show you. On GPT-4o-mini every one of the eight three-constraint prompts scored below what its own parts predicted, the worst by 12.2 points, and JSON was about twice as costly as XML. On the GPT-4.1 family the same stack costs nothing at all. The damage is a property of the model you happen to be on, and of the prompt as a whole — not of any line in it.
The design is deliberately mundane. Three things that get bolted onto a production code-generation prompt, three levels each: how the output must be shaped, who the model is told it is, and how much pressure the request carries. Twenty-seven combinations, every one of them run against the same 164 problems, with greedy decoding so nothing moves between runs except the wrapper.
The scoring separates two ways a run can fail. A format-aware extractor pulls the code back out of whatever envelope was requested, so a model that wrote a correct function but broke the JSON is counted as a formatting failure rather than a reasoning one. Both still count as a failure of the call — which is also what happens in your service — but the split means the paper can say which kind of damage a constraint does.
Look at that spread before anything else. On the two GPT-4.1 models the wrapper is worth about six points end to end — noise you would never chase. On GPT-4o-mini it is nearly fifteen, and on the reasoning model it is thirty-two. Whether prompt shape matters at all is itself a property of the model.
This is the part that makes the result awkward. Take the same 22,140 runs and average them the ordinary way — all runs with JSON against all runs without, all runs with an expert persona against all runs without — and the constraints look small and mostly benign. A couple of points here, a couple there. Nothing you would write a ticket about.
Urgency framing, read this way, is mildly positive on every model tested — telling GPT-4o that production is down is worth about three points over saying nothing. XML output is positive too. An expert persona is worth roughly nothing. If you ran the obvious ablation, one factor at a time, you would conclude that this whole family of prompt decorations is a rounding error and move on.
Here is the arithmetic the paper hangs on. Take the bare baseline, add the three single-factor effects you just measured, and you have a prediction for what the combined prompt should score. Then measure the combined prompt. The difference between the two — what the parts said would happen, and what happened — is the interaction. If constraints were independent it would be zero.
On GPT-4o-mini all eight three-constraint prompts land under their prediction, by 7.6 points on average and 12.2 at the worst — a JSON envelope, an expert persona and a be-thorough line, three things nobody would think twice about shipping. The format asymmetry is stark: JSON combinations average 10.7 points below prediction, XML combinations 4.6. Whatever the JSON envelope costs the model, it costs more when there is other instruction in the way.
GPT-4o is the interesting middle. Its JSON combinations are nearly additive — within a point, one of them slightly positive — while its XML combinations are the ones that break, running 6.7 to 8.5 points under prediction. Same vendor, same generation, opposite failure surface. There is no rule here you could carry from one model to the next.
The gaps are large enough to survive a significance test rather than being an artefact of 164 problems. On GPT-4o-mini, the best single-constraint prompt against the worst triple is an odds ratio of 3.67 with a 95% interval of 1.49 to 9.04 and p = 0.004. On GPT-4o, moderate urgency alone against JSON with a generic persona gives an odds ratio of 6.25, interval 2.18 to 17.96. On GPT-4.1-mini no pairwise comparison reaches significance at all.
The natural guess is that small models are brittle and large ones are robust — that this is a capacity problem you buy your way out of. The data does not support it. GPT-4o-mini and GPT-4o differ substantially in size and both degrade. GPT-4.1-mini and GPT-4.1 differ by the same kind of gap and neither does. The line falls between the two families, not across the size axis inside them.
The fifth model goes the other way entirely, and it is worth a paragraph on its own. o3-mini is the weakest of the five when you hand it a bare prompt and the strongest of the five once you constrain the output. A structured-output requirement does not compete with its reasoning; it appears to organise it.
So there is no safe default. "Always ask for JSON" is right on one of these five models, roughly free on two, and expensive on two. The only thing that transfers between them is the method: measure the prompt you are actually going to send.
The practical shape of this is a testing problem, not a prompting one. Almost every prompt-quality process in production tests factors: someone changes the persona line and reruns the eval, someone adds a JSON envelope and reruns the eval. Each change passes. The prompt that ships is the sum of all of them, and nobody ever ran that one.
The full grid gets expensive fast, and the paper does not claim you need it. What it establishes is that the single-factor result is not evidence about the compound one, so the minimum honest test is the prompt as assembled. Pick a request and compare the two habits.
The scenarios above are illustrative — the paper measures prompts, not release processes. What it measures is the premise underneath them: that a constraint's effect measured alone tells you close to nothing about its effect measured in company, on at least two of five widely used models.