An extension of Scheffe's (1959) confidence bounds gives sharp confidence bounds for a linear function of non-negative arguments. The length of these bounds is compared with that of the conservative Scheffe bounds which would usually be used in this situation. A table facilitating application of the sharpened bounds is provided
On Sharpening Scheffe Bounds
Bohrer, R. (1967). On Sharpening Scheffe Bounds. Journal of the Royal Statistical Society. Series B (Methodological), 29(1), 110-114.