The Supreme Court is considering how to resolve a long-running legal fight between Kansas and Nebraska over the use of water from the Republican River.

The justices on Tuesday appeared to agree with recommendations of a special master who found Nebraska should pay $3.7 million in damages to Kansas for using more than its legal share of the river’s water in 2005 and 2006.

But they were more doubtful about making Nebraska pay a $1.8 million penalty that exceeds Kansas’ actual damages. The justices also seemed skeptical about Nebraska’s push to change the formula for measuring water consumption. Nebraska says the formula is unfair.

The dispute centers on a 1943 compact that allocates 49 percent of the river’s water to Nebraska, 40 percent to Kansas and 11 percent to Colorado.