I find Lands' End's tailored fit shirts still too big around the waist, and wound up having mine darted. I have an eight-inch drop (38/30).
I've found two brands that fit me nicely, though they aren't necessarily budget.
1) Haupt fashion fit - These run small. I normally wear 15/33 but had to go up half a size (15.5/34) to get a good fit, then get the sleeves shortened. Armholes aren't particularly high but there's very little extra fabric around my waist.
2) Etro - Nice fabric, very good fit and high armholes. Worth getting when on sale, but even then might not be cheap.