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UPDATE 2/2 2:45pm - (TMZ) - Bobbi Kristina -- who was revived from death over the weekend -- is now doing significantly better -- according to TMZ -- but it's still touch and go.

Sources connected with the family tell TMZ ... doctors performed tests Monday morning and determined the swelling on her brain has gone down. In addition, she has been able to "move her eyes" ... all important signs. 

Perhaps most important ... TMZ reports the oxygen levels in her brain have increased significantly -- 4 times better than Sunday.

TMZ also reports the family has been told ... because Bobbi Kristina was deprived of oxygen for anywhere between 2 to 5 minutes while she was submerged in a tub, doctors fear neurological damage.


(TMZ) - Doctors saw a slight glimmer of hope for Bobbi Kristina Monday morning -- but they remain clear she's not out of the woods, reports TMZ. 

[REALTED - Bobby Brown Asks For Privacy Following Daughter's Hospitalization]

Sources connected to the Houston family tell TMZ ... doctors were testing Bobbi's brain reaction to different stimuli, and saw "minimal response" during one of the tests. TMZ reports doctors view this as a very slight improvement -- but it's enough to delay any immediate discussion of turning off life support.

As TMZ reported over the weekend ... the situation has been bleak, and -- according to TMZ -- just last night the family started discussing funeral arrangements.

[RELATED - TMZ: Bobbi Kristina Brown Found Unconscious In Bathtub, Revived & Breathing Again]

Bobbi Kristina's been in a medically induced coma since Saturday ... when she was found unconscious in her bathtub.


Photo: Splash News