Yesterday I started with letting Fluffy run through my workroom, the same place where her cage is. At first, she was a bit scared, but now she's running around happily. She's sniffing and biting and climbing and running (especially running) and she has a great time. I really notice it, she's much happier now than she was. She's still very tame and want to be petted often (at times, she comes to my chair and nudges my feet and ankles with her nose, like saying "Hey, pet me!") but not as long as before.
I draped all wires in the air (as good as possible), so she can't get to them. Tonight I'll post some pictures from her running around. It's really cool.