Short-form supplemental essays — common at MIT, UChicago, Columbia — are harder to write well than longer essays precisely because there's no room for inefficiency.
The Compression Principle
A 150-word essay should convey the same thing as a 650-word essay: something specific and true about who you are. The difference is that the 150-word version has no room for build-up, context-setting, or extended reflection. You must arrive immediately at the most specific, compelling element of what you want to say — and stay there.
Lead With Your Best Detail
In a longer essay, you might spend the first paragraph setting a scene. In a short essay, the first sentence should be your best sentence — the most specific, most vivid, most revealing element. Don't build to the interesting part; start there.
One Idea, Developed Well
The most common failure in short essays is trying to introduce three ideas in space that can only support one. Choose the single most important thing you want to convey and develop it as fully as the word limit allows. A single idea explored specifically is far more compelling than three ideas mentioned superficially.