What's the best way to strain stock? I have a big pot full of chicken necks and backs on the stove which I need to separate into (a) stock and (b) everything else.

I'm wondering the best way to go about doing this. I've previously laid cheesecloth into a fine-mesh strainer and poured it through that, but the cheesecloth always seems to kind of clog up, making straining 4 litres of stock a very lengthy process. I also tried a coffee filter laid inside a strainer and got more-or-less the same results. 

Alternatively, I ditched the cheesecloth and just used the fine-mesh strainer by itself, but, unsurprisingly, this method leaves some bits I'd rather not have. 

I'm wondering: is there a better way? Or should I stick with the cheesecloth and work on being more patient?
Perhaps you could consider straining it twice? Use your strainer the first time to get out the larger particles and then do a second time with the cheesecloth so that it doesn't get clogged as easily. I imagine this wouldn't be any faster, but you'd have to fight with the clogged cheesecloth less.