I have a compaq presario 6016us that comes with a 220W power supply. other installed components are 1 sata card, 1 wd green drive 1tb, 1 cd/dvd burner, and 1gb mem.
I bought the Sapphire 3850. I have been running for a month or so fully stable. It comes with a Molex to 8pin P8 adapter with 2 molex connectors which I was careful to run two different lines coming from the power supply. There are several web sites that indicate that the maximum wattage for this card is right around 70 watts. http://www.xbitlabs.com/articles/video/display/gigabyte-radeonhd3870-3850_5.html#sect0