Have any of you ever rappelled with 3mm cord?
If not, be sure to consider how to rig your rappelling/belay device (rack or Figure 8), I suspect that there would be insufficient friction with the standard configuration on an 8 (you may have to doubled or even triple wrap the device) and be sure to start with all of the bars on your rack in place. While the 3mm and even the 5mm cord may have significant weight loading capacity, the reduced diameter (note: on regular low stretch/static rope, the rope will flatten at the point of contact with the belay device, thus increasing the surface area/friction) may not provide sufficient friction to maintain a controlled rappel. Many of the other auto-descending devices may not work at all with 3 or 5 mm rope. Be sure to check with the manufacturer of the device before varying the rope diameter, otherwise you may receive a nasty surprise when trying to rappel during an emergency situation.
Pete