Bobbi Kristina Brown reportedly has shown some key signs of improvement, although a statement issued by her family says she's "fighting for her life."

[Full coverage of Bobbi Kristina's medical emergency]

Bobbi Kristina posted this photo of herself and her husband Nick Gordon last fall.

Credit: Jennifer Brett

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Credit: Jennifer Brett

TMZ, quoting a source close to the situation, said Bobbi Kristina has been able to move her eyes and that swelling on her brain had abated. She'd been placed in a medically induced coma to address the swelling.

A statement issued by the Houston family asked for prayers and privacy: "We are asking you to honor our request for privacy during this difficult time. Thank you for your prayers, well wishes, and we greatly appreciate your continued support. "

An earlier statement released on behalf of Bobby Brown also requested privacy. Click here to read his entire statement.

A newly released police report shows that the emergency call on Saturday went out as a "drowning" call. Click here for more details.

Family members have been gathering at the hospital ever since, possibly setting up a tense situation. Last year, one of Bobbi Kristina's relatives took out a restraining order on her husband, Nick Gordon, court documents show. Details here.

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