Money has always made a big difference in the medical world: fancier rooms at hospitals, better food and access to the latest treatments and technology. Concierge practices, where patients pay several thousand dollars a year so they can quickly reach their primary care doctor, with guaranteed same-day appointments, have been around for decades. But these aren’t the concierge doctors you’ve heard about — and that’s intentional.

As with the ever more rarefied tiers of frequent-flier programs or V.I.P. floors at hotels, the appeal of MD Squared and Private Medical is about intangibles like time, access and personal attention. “I am able to give the time and energy each patient deserves,” said Dr. Matles, the MD2 physician in Menlo Park. “I wish I could have offered this to everyone in my old practice, but it just wasn’t feasible.”

Dr. Howard Maron, who founded MD2, is similarly candid about the new reality of ultra-elite medical care.

“In my old waiting room in Seattle, the C.E.O. of a company might be sitting next to a custodian from that company,” he recalled. “While I admired that egalitarian aspect of medicine, it started to appear somewhat odd. Why would people who have all their other affairs in order — legal, financial, even groundskeepers — settle for a 15-minute slot?”