Conan O’Brien’s second night on “The Tonight Show” exhibited signs of improvement but indicated that the host is still finding the new program, the raucous audience response and extended ovations notwithstanding.

The monologue again proved slightly uneven, as did a taped piece in which O’Brien went on a shopping spree through the Crenshaw district. Oddly enough, the real highlight came courtesy of Brian Williams’ interview with President Obama, who spoke earnestly about the Leno-to-Conan transition, promising that there would be no bailout.

The one major area of improvement on Tuesday had little to do with the host, as Tom Hanks did pretty much everything you can ask of a talkshow guest: He was witty, engaging, prepped with good stories (including a Ron Howard impersonation that made the director sound like an early Jerry Lewis), and even expressed human-sounding enthusiasm for a local burger chain.

O’Brien also showed flashes of his ability to create the show at the desk, with a small bit about his California driver’s license photo that generated solid laughs. The more he can do that — without feeling the need to rely on elaborate taped pieces — the better off he’ll be. By contrast, a spoof about Twitter had promise but went nowhere.

Still, if you were scoring on points, the referee’s decision again went to David Letterman. He delivered a firstrate monologue and again joked about the latenight turmoil over at NBC, including an aside about North Korean dictator Kim Jong-Il being offered “the 10 o’clock slot” to make him go away.

So all told, a pretty good night for Conan — but a better one for Dave. The real question will be how well the “Tonight Show” numbers hold up from Monday after the initial burst of curiosity. O’Brien has a golden opportunity to woo fringe voters, as it were, over the next few weeks — but the real test for NBC will come in the fall, when Leno shakes up the 10 p.m. hour.

Until then, savor those ovations.