Kelsey Grammer by Jason Kempin/ WireImage.com Kelsey Grammer by Jason Kempin/ WireImage.com

As well-wishes and support from fans and costars such as Swing Vote's Kevin Costner pour in, Kelsey Grammer continues to recover from the faintness which landed him back in the hospital several weeks after he suffered a mild heart attack.

"Kelsey is just fine," his publicist, Stan Rosenfield, tells TVGuide.com. That said, Grammer's camp has decided to curtail further detailed updates, and instead let the next big news be the good word that the beloved TV vet is well enough to return home. "We will let you know when he leaves the hospital," says Rosenfield.

Grammer was promoting Swing Vote in New York when he felt faint and was taken to the hospital as a precaution/for observation. By some accounts, his heart medication could have been to blame. - Matt Mitovich