Veep” has actually gotten considerable mileage out of what amounts to a one-note-joke premise — the indignities of being vice president visited upon a politician who mixes unbridled ambition with an utter lack of convictions. It’s essentially the comedy companion to “House of Cards,” buoyed by Julia Louis-Dreyfus’ fearless irreverence in the central role. This season finds her character charting a bid to become president, providing greater cohesion and drive to the storytelling. As for how that will work out over the long term, well, it’s hard to see them changing the name of the show to “POTUS.”

Louis-Dreyfus’ Selina Meyer is still reeling from the yet-to-be-publicly revealed news that the always-unseen president won’t seek reelection as the season begins. Gradually, she seeks to line up support by scheduling a book tour (in Iowa, naturally) for an autobiography she didn’t write, filled with platitudes she can barely stomach.

In the premiere, that means she has to miss the wedding of her spokesman Mike (Matt Walsh), although the plot thickens considerably in the second episode, when the president amends his position on abortion, a hot potato Selina has no interest in handling, dubbing the president’s action, “The unflushable turd that is left in the can for the next person.”

In a way, that episode perfectly encapsulates some of what’s good about “Veep” — it’s ruthlessly funny, as created by Armando Iannucci and portrayed by Louis-Dreyfus — but also what remains a tad too precious, tiptoeing around issues of party allegiance, which seems increasingly improbable as the Meyer campaign forges onward. The same goes for a subplot that has former White House operative Jonah (Timothy C. Simons) trying to make a go of it as a political blogger.

That said, the election plot gives the series additional narrative momentum, including the internal jockeying for roles in the nascent Meyer campaign, and with the addition of guests like “The Wire’s” Isiah Whitlock Jr. adds heft to a cast already buttressed by Kevin Dunn and Gary Cole joining the party after the first season.

Amid the show’s jaundiced view of politics, the new season also brings an episode in which the vice president and her entourage visit Silicon Valley, offering a pretty amusing image of Ping-Pong-playing programmers and spaced-out billionaires that dovetails rather neatly with the show’s new lead-in, “Silicon Valley.”

“Veep” has earned enough critical and award-circuit plaudits (including Emmys last year for Louis-Dreyfus and Tony Hale) to qualify as a winner for HBO, even before throwing in the inside-the-Beltway angle, which tends to yield a multiplier effect in terms of media coverage beyond the usual suspects. And the show does have an unpretentious quality that’s somewhat refreshing amid the recent spate of D.C.-centric series.

Even so, “Veep” remains pretty well defined by its protagonist’s inherent plight: noteworthy, yes, but still a significant step away from true greatness.

TV Review: ‘Veep’

(Series; HBO, Sun. April 6, 10:30 p.m.)

  • Production: <p class="BodyText_Justified">Filmed in Maryland by Dundee.</p>
  • Crew: <p class="BodyText_Justified">Executive producers, Armando Iannucci, Christopher Godsick, Frank Rich; co-executive producers, Simon Blackwell, Tony Roche; producers, Stephanie Laing, Julia Louis-Dreyfus; director, Chris Addison; writers, Sean Gray, Will Smith; story by Iannucci, Gray, Smith; camera, Jay Feather; production designer, Jim Gloster; editor, Billy Sneddon; music, Rupert Gregson-Williams, Christopher Willis; casting, Allison Jones. 30 MIN.</p>
  • Cast: <p class="BodyText_Justified">Julia Louis-Dreyfus, Tony Hale, Anna Chlumsky, Reid Scott, Matt Walsh, Timothy C. Simons, Sufe Bradshaw, Kevin Dunn, Gary Cole</p>
  • Music By: