Since mining works fine in a 1x PCIe slot, why not go even slower with the conventional PCI bus?
I bought one of these adapters for testing ($28 incl. shipping on Ebay) and it seems to work fine. HD5870 at 900 MHz gives 354 Mhash/s, which is no different from running it in a 16x PCIe slot. Now I can fit even more cards in this single mobo
There are just a few practical considerations. PCI is a shared bus, so performance may go down with more than one of these adapters. Also, PCI only gives 25 W of power, vs. 75 W of PCIe, but this does not seem to be a problem when the card is powered externally. Mounting the card is yet another issue, since this is basically a riser card.
Also, X refused to start in the usual way, but it worked after setting BusID explicitly. In my case, it was
BusID "PCI:6:0:0"
The exact number can be seen from lspci, in a slightly different format like 06:00.0 in this case. The line goes in the Device section of xorg.conf.
(using Linux 2.6.37.5, fglrx 10.12, SDK 2.1)