As a quasi-minuscule representation has a zero weight, its weights must be in the root lattice. Since every non-zero dominant weight is positive on at least one simple root, the quasi-minuscule condition implies that non-zero weights are in fact roots. There is only one orbit of them, so in case there are different root lengths, the long roots are excluded. In summary, for every simple type there is a unique quasi-minuscule representation, and the unique dominant short root is its highest weight.