Things appear to be looking up for Joan Rivers, who has been in the hospital since last Thursday, placed in a medically induced coma after she stopped breathing during throat surgery. A source told E! News that the comedian is “on the road to recovery,” after doctors began the process of waking her from her coma on Sunday. The source added that “She’s getting better, don’t believe the ridiculous hype.”

The situation was looking dire for most of the weekend after the star was rushed to Mt. Sinai hospital, and almost immediately put on life support. It was reported that doctors feared Rivers would suffer permanent brain damage, possibly losing a great deal of her motor skills. At one point, reports surfaced that the comedian’s daughter Melissa, who was faced with the possible decision of whether or not to keep her alive, was considering a lawsuit against the surgeon who performed the initial surgery, for medical malpractice. The E! source now says “she is making small but positive steps,” and doctors expect to be able to gauge the extent of Rivers’ brain function by later today.

The source told the network that the Melissa has been handling the situation remarkably well. “She is a rock,” the source says.  “She’s calmer than I have ever seen her. All these reports about doomsday are not true. She is her mother’s daughter and she’s tough as nails.  She’s the person keeping everyone together.”

The younger Rivers, meanwhile, has released her own statement saying, “On behalf of my mother and our family, we are extremely grateful for all the love and support we’ve received. At this time she does remain on life support. I know my mother would be overwhelmed by the continued outpouring of kindness, and I want to thank everyone for keeping us in their prayers.”

The comedian had been scheduled to cover the upcoming New York Fashion Week on her show, Fashion Police, but that has been cancelled. It is unclear, as of yet, whether she will be able to resume hosting the show once she is more recovered.