You can do better than that. If the distance between the two data points is 7⁄4, you can shrink the 100% confidence interval to 1⁄4, etc. (The extreme case is as the distance between the two data points approaches 2, your 100% confidence interval approaches size zero.)
EDIT: whoops, I was stupid. Corrected 3⁄4 to 7⁄4 and 1 to 2. There, now it should be right
You can do better than that. If the distance between the two data points is 7⁄4, you can shrink the 100% confidence interval to 1⁄4, etc. (The extreme case is as the distance between the two data points approaches 2, your 100% confidence interval approaches size zero.)
EDIT: whoops, I was stupid. Corrected 3⁄4 to 7⁄4 and 1 to 2. There, now it should be right