We are convinced that besides writing down the purpose (P=Purpose) it makes a lot of sense to explicitly ask about the benefits (A=Advantage), as well as to ask about measurability (M=Measure), how you know if you have achieved the goals.

But if you want to write down less, then we suggest to write down only the purpose, but at least talk about benefits and measurability with stakeholders (including the development team, of course). This way the documentation will be minimal, but the other essential content (A and M) has at least been discussed and communicated verbally.