I didn't think the D3s had this problem, or at least didn't have the complex multi-chamber venturi driven tank system.
It's one of the only issues I still haven't resolved on my D2, after about 4 years of ownership, and it's not through lack of trying. I've had a go myself and had a dozen mechanics attempt the repair, including 1 or 2 pretty skilled ones, but I haven't been able to fix it yet. I've just learned to live with it and always keep it above half a tank. I'm considered locating a suitable replacement tank, complete with pumps.
The problem with my car began when I bought it: Typical backstreet car sales place, made sure there was just enough fuel in their vehicles to keep the bottom of the tank wet, and not a drop more. They managed to let it run out and subsequently damaged the pump, which they had repaired by a local backstreet garage, who I think probably cracked some part of the tank receptacle for the pump housing. I discovered the problem shortly after buying it, but I was reluctant to take the car back in case they broke something else.
Hopefully yours will be an easier fix. If it's anything like working on the D2 system and you're thinking of attempting it yourself, prepare to spend several hours cramped up in the boot, high on petrol fumes, cursing and swearing with screwdrivers in one hand and an endoscope in the other.