Teachers, principals, progressive education advocates, and a host of others say that students take way too many standardized tests these days. And Gov. Dannel P. Malloy of Connecticut, a Democrat, seems to agree, at least when it comes to eleventh graders in the Nutmeg State.

Earlier this month, Malloy sent a letter to U.S. Secretary of Education Arne Duncan, saying that he wants to “start a dialogue” between the feds and Connecticut on ways to “reduce the testing burden.” He thought Duncan might be receptive to this argument when he read this back-to-school commentary posted on the U.S. Department of Education’s website, in which he says he’s gotten the message that testing takes up too much time.

Malloy isn’t making a pitch for any super bold changes to the testing regime, such as replacing tests with performance tasks or assessing students in certain grade spans, as opposed to annually in grades 3 through 8 and once in high school. (Staggered testing is an idea that at least a handful of members of Congress favor.)

But he’s considering allowing eleventh graders who, he writes, may be among the most overtested students, to take the SAT, a college entrance exam, during the school day, in lieu of the Smarter Balanced high school exam. The SAT was recently revamped to align more closely with the Common Core. If Connecticut decides to move in this direction, it would have plenty of company. Maine uses the SAT for accountability purposes, but plans to switch to the Smarter Balanced high school test when that becomes available. And other states, including Kentucky, have built the ACT and related exams into their accountability systems.

Malloy’s not sold on this solution, writing that it will require further study. But it’s interesting, at least rhetorically, that he wants to explore solutions for reducing testing—and wants Duncan’s collaboration with that task.