Britney Spears just showed up in Kansas City, Missouri for her second round of "X Factor" judging ... and so far, not a SINGLE meltdown -- though there was a rocky entrance.

Brit stumbled in her high heels as she exited her limo, but quickly recovered ... to begin her first judging gig since San Antonio two weeks ago -- when Britney mysteriously walked off set and disappeared for several acts.

We're told Britney's bringing her A-game today -- showing up on time in a sexy white dress and signing autographs for adoring fans.

That's not to say things are going perfectly -- Simon Cowell is a no-show today due to a bad case of bronchitis. UK "X Factor" judge Louis Walsh is filling in.

L.A. Reid and Demi Lovato were also there.


We're told Britney was especially tough with Simon absent -- and the shocking audition of the day went to an Elvis wannabe who told, "Your look was a little much, and everything was messed up. But I found you interestingly entertaining."