Can someone that owns a later-model W140 with factory Xenon headlamps tell me what size fuse is spec'd for the headlamps?

I recently scored a set of OEM Xenon headlamps on eBay. They were sans-bulbs, but for the price I paid, I didn't care.

Should point out car has been sitting for a loooong time and the battery voltage was very low (10.38 at the headlamp connector).

Lamp ignited fine, but as it warmed up, the fuse popped. (Maybe 2-3 seconds after fire-off).

Started the car and got 13.3 at the lamp harness. Fitted a new 15a fuse which is all I had handy. The fuse chart says the fuse should be 7.5A and that's what was mounted when it blew. With the 15A fuse the same lamp lit and stayed on just fine.

The bulbs say 35W on them (which equates to 2.91a @ 12v) , but I'm fairly sure the light-off draw is far higher than 35W.

I've not tested the lamps for draw - that's my next step just to make sure I don't ruin something.

Regardless - I still need to know what the fuse rating is for a car with factory mounted lamps. If I need to rewire for these lamps, it would be nice to know sooner rather than later.