Awkward, unseemly, shame-on-him (and shame-on-the-media) moments of news-conference theater, playing on live television in the late afternoon, used to happen about two or three times a year.

Now they seem to occur about once every two weeks, and the cultural chronic fatigue syndrome you’re feeling about these sex (and sext) scandals is quite real. I share your pain. The wiener jokes have all been made and not one of them was ever that funny. The tut-tutting moves at the speed of Twitter.

Still, the Monday afternoon news conference summoned by Rep. Anthony Weiner (D-N.Y.) at a Sheraton hotel in New York so he could finally admit — in that sheepishly embarrassed, Eugene-from-“Grease” voice of his — that those gray boxer briefs and the tumescence they contained were indeed his, was remarkable for its utter shabbiness of spirit and setting. This stuff is a total drag to watch; anyone taking delight in it needs a media cleanse and several weeks’ stay at a monastery with no electricity or broadband.

That awful blue drape, the drop-panel ceiling. The sweaty reporters. The manufactured outrage and strange episode of pre-presser microphone hijacking by micro-mulleted blog don Andrew Breitbart, whose conservative news site first called attention to Weiner’s errant tweet that started this mini-saga. Breitbart’s “Kanye” move was followed, much too belatedly, by Weiner’s choked-tears appearance and his endlessly repetitive use of our era’s empty-apology vernacular: regret, deeply regret, full responsibility.

So there it was. The whole story, or perhaps the whole story, that nobody wanted but everyone covered. (They do this about 1,000 times better on CBS’s “The Good Wife,” so why look at all?)

"CBS Evening News" anchor Scott Pelley, 53, was and is the finest correspondent on “60 Minutes.” (JOHN PAUL FILO/AP)

When it was over, CNN afternoon anchor Brooke Baldwin said that the network had “intended to cover the breaking news of those five American men” killed in Iraq, intended quite nobly to cover it for the previous hour or two — only, but, well, you know how it is. Now Baldwin handed the talking stick to Wolf Blitzer, to whom Weiner had personally lied about the boxer briefs just days ago . . . and boy, Blitzer did not look happy. He had assembled a bevy of salivating pundits in “The Situation Room,” ready to sear Weiner’s political future to a crisp.

As I said: To a monastery with all of you. No electricity. (No porn, no tweets, no Wolf.)

Meanwhile, I saw a ray of serious sunshine on the future of TV journalism. Barely an hour later, CBS calmly and with little fanfare debuted “The CBS Evening News With Scott Pelley.” That would be the network’s not-ballyhooed, post-Katie Couric nightly newscast.

Little has changed, but as promised, it came with a “60 Minutes” flavoring befitting the fact that Pelley, 53, was and is the venerable newsmagazine’s finest correspondent.

Showing a restraint that, say, “NBC Nightly News” could not (“The age of oversharing has claimed another man,” Brian Williams intoned, leading off his newscast with Weinergate), Pelley and company went to a long, on-the-ground report from Afghanistan, where reporter Mandy Clark had embedded with Army soldiers fighting on the Pakistan border. That led to six or so minutes connecting the future of the American involvement in Afghanistan to the troop killings in Iraq.

Now Weiner?

No. Pelley then segued to a long story about recent breakthroughs in treating melanoma and lung cancer.

Nine minutes in — now Weiner? No, not until after the first commercial break, when Pelley granted the congressman’s apology a full minute clip, followed by some analysis from Capitol Hill correspondent Nancy Cordes, who essentially boiled the drama down to a rather grown-up summary of why some politicians recover from this kind of scandal and some don’t. That was followed, fittingly, by the latest news about former International Monetary Fund head Dominique Strauss-Kahn’s rape charges.

Then came a quick item on Rick Santorum’s official bid for the 2012 Republican nomination; more glum news about the housing industry; Steve Jobs’s iCloud; the Arizona wildfire; and finally, a long and uplifting feature about a World War II veteran’s trip to Normandy after 67 years.

None of that was any better than when Couric was anchoring mere weeks ago. I don’t know why (or even whether) it brings viewers any more comfort to have the news anchored by a stern-jawed man with graying hair, but Pelley’s initial broadcast reminded me of how reliable and elegant the nightly news can be — and how nice it would be to sit in a recliner at 6:30 every night and just let the news be news. Of course it feels old, yesteryear, outmoded. (Plavix is not for everyone. Ask your doctor.)

But it felt dependable, too. Weiner was everywhere (deeply regret; deeply deeply; full responsibility — I get the feeling he’s still in a dark room somewhere, repeating it over and over still), but Pelley took the high road. The sound you hear is the sound of Edward R. Murrow remaining, for once, completely still in his grave.