Can I have multiple valid ESTAs in different passports?

I'm a citizen of country X and have a valid United States ESTA in my X passport. Recently, I became of citizen of Y and now have a Y passport as well, which I would like to use for future travel to the US. Both countries qualify for the Visa Waiver Program. Can I have ESTAs in both passports at the same time?

The official CBP site seems contradictory, first implying that I should get a new ESTA:

If you obtain a new passport or change your name, gender or country of citizenship, you will be required to apply for a new travel authorization. This is also required if one of your answers to any of the VWP eligibility questions changes. The associated fee of $14 will be charged for each new application.

And then saying that I should not have two simultaneous ESTAs:

If you have dual citizenship and have registered with ESTA, you should use your VWP-eligible passport to board the plane when you leave your country of departure and when you arrive in the U.S. If both your countries of citizenship are VWP-eligible, then we strongly recommend you choose which one you want to claim for purposes of travel to the U.S., and use that country's passport each time you travel. One person with two different ESTA authorizations creates confusion that will only delay your travel.

Cancelling the old ESTA would seem a valid way to fulfill both requirements, but there doesn't appear to be any way to do this?