Here's Sapphire's recommendations for a 3850 or a 3870, but doesn't reveal much

System Requirement:
PCI Express based PC is required with one X16 lane graphic slot available on the motherboard.
1GB or greater system memory for better performance.
450Watt or greater power supply with 75 Watt 6-pin PCI Express power connector recommended.
For ATI CrossfireX: 550 watt power supply or greater with two 6-pin connectors.
Certified power supplies are recommended. Refer to
http://ati.amd.com/certifiedPSU for a list of Certified products
Installation software requires CD-ROM drive.
DVD playback requires DVD driver
Blu-ray/HD DVD playback requires Blu-ray/HD-DVD drive and playback software.
For a complete ATI CrossFireX? system, a second ATI Radeon? HD 3850 graphics card, an ATI CrossFireX Ready motherboard and one ATI CrossFireX Bridge Interconnect cable per board are required.
If you look at the link below, it shows that the 3850 consumes about 5w less than a 8600gts. So there isn't too much power needed, about 181w for the TOTAL system (which was measured at the wall).
http://techreport.com/articles.x/13603/9
And this too:
Power consumption
It's time to do some actual testing with these cards. We'll start off by showing you some tests we have done on overall power consumption of the PC. Power consumption is a big thing, and I'm thrilled to see what AMD has achieved here.
Looking at it from a performance versus wattage point of view, the power consumption is really good with the new 55nm products. Our test system is a Core 2 Duo X6800 Extreme Processor, the nForce 680i SLI mainboard, a passive water-cooling solution on the CPU, 2GB memory, DVD-ROM and WD Raptor drive. Have a look:
Videocard
System Under load
8800 Ultra
371 Watt
HD 2900 XT
391 Watt
HD 3870 286 Watt
HD 3850 246 Watt
Observe closely the difference between the 2900 and the 3870. Shocking as performance is nearly equal while wattage dropped over a 100 Watts. A big thumbs up to AMD here, that's just brilliant.
The methodology is simple: we look at the peak wattage during our benchmark session to verify power consumption. It's a good load test as both GPU and CPU are utilized really hard here. Please do understand that you are not looking at the power consumption of the graphics card, but the consumption of the entire PC.
In my view the Radeon HD 38xx series require you to have a 450 Watt power supply unit at minimum if you use it in a high-end system, and I think that's barely on the safe side. Also recommended is 28 AMP's on the 12 volts rails for stable power distribution (on a single card configuration)
http://guru3d.com/article/Videocards/472/8/
You can check them out and see what you think.