There was a moment during Tuesday's Republican town hall event in Milwaukee when a voter stood up and asked Ted Cruz to name his greatest personal failing. CNN moderator Anderson Cooper decided to volunteer his own, too: "My greatest failing is sometimes I don't follow up."

Not on Tuesday. Cooper was cordial but relentless as he pressed the candidates — particularly Cruz and Donald Trump — to explain their positions, to stay on topic, and to stop acting like children.

"But, sir, with all due respect, that's the argument of 5-year-old," Cooper told Trump when the GOP front-runner protested that he "didn't start" last week's shameful feud with Cruz that involved both candidates' wives.

The remark highlighted an exchange in which Cooper performed the exhausting task of interjecting every time Trump said something distorted or untrue. Referring to the tweet below, Trump said he "thought it was a nice picture of Heidi" Cruz.

"Come on," Cooper shot back.

Moments later, referring to a social media ad campaign by a super PAC called Make America Awesome, Trump stated that it was Cruz who "sent out a picture."

"He didn't send out a picture," Cooper corrected. "It was an anti-Trump super PAC that sent it out."

So it went for much of the evening. This was tough work for several reasons. Broadcast interviewers are trained not to interrupt; the best are masters of nonverbal cues that let subjects know they're engaged, or have something to say, without muddying the air with "uh huhs" or cutting off soundbites.

Butting in as often as Cooper did in Wisconsin required him to abandon conventional principles. It was also hard because of the sheer volume of Trump's misleading claims and because the billionaire hates to be interrupted. He's always ready to take back control of the conversation with a forceful "excuse me."

In fact, Trump wound up dropping 18 "excuse mes" on Cooper in one hour.

It wasn't just real-time fact-checking that made Cooper's session with Trump so good. He also showed an ear for subtle inconsistencies and refused to let them slide. For example: a voter asked Trump to list what he considers the top three functions of the federal government, and the candidate named national security, education and health care. That's a fine priority list — except that Trump wants to repeal Obamacare -- which increased government's role in health care -- and has railed against the federal government's role in education. What the heck was he talking about here? Cooper resolved to find out.

COOPER: Aren't you against the federal government's involvement in education? Don't you want it to dissolve to states?

TRUMP: I want it to go to states, yes. Absolutely. I want — right now ...

COOPER: So that's not part of what the federal government's ...

(CROSSTALK)

TRUMP: The federal government, but the concept of the country is the concept that we have to have education within the country, and we have to get rid of Common Core, and it should be brought to the state level.

COOPER: And federal health care run by the federal government?

TRUMP: Health care — we need health care for our people. We need a good — Obamacare is a disaster. It's proven to be ...

COOPER: But is that something the federal government should be doing?

TRUMP: The government can lead it, but it should be privately done.

This was first-rate nonsense. "The concept of the country is the concept that we have to have education within the country?" It should have been obvious to anyone paying attention that Trump's policy prescriptions are pretty vapid.

Emphasis on should. Neither Cooper nor the media at large can foist conclusions on voters, but this was a terrific example of a journalist doing his job — asking tough, illuminating follow-up questions.

Cooper was equally sharp in his hour with Cruz. One of the best exchanges centered on the Texas senator's statement last week that "we need to empower law enforcement to patrol and secure Muslim neighborhoods before they become radicalized." The remark was a classic case of tough talk that a candidate would rather not explain in any detail. So Cooper asked Cruz what he meant four times and repeatedly pointed out that the closest analogue for his proposal — a surveillance program piloted but ultimately abandoned by New York police — didn't work, according to that city's police chief.

Cruz insisted, against all evidence, that "this was a successful program," and Cooper didn't let him get away with it.

In another moment, when Cruz launched into a complaint about how much "free media" cable news networks have given to Trump, Cooper responded with this: "Well, I got to say, we've asked you for interviews pretty much every day, and you've declined every offer on my program."

It was easy to see why on Tuesday. Cruz was visibly frustrated by Cooper's doggedness.

Others loved it, though — and for good reason. Cooper's assertive, cut-the-crap questioning is exactly what this campaign needs more of.