When I read comments like "he cries in our arms so heaven knows what he'll be like when we put him down", I just think, put him down then. He's crying while you're there, maybe he actually wants to be on his own?
When you know your baby you know when it is a hungry cry or something the matter instead of just a "I've woken up, where am I? How do I get back to sleep again? Oh, now I remember zzz" cry.
In my view if the baby is fed, warm and clean and is crying around the time they usually sleep and rocking, cuddling and cooing isn't helping maybe they just want to be left in peace. So put them safely in a cot, leave the room and go somewhere you can't hear for 10 minutes. They will be asleep in that time and no less. If they're not then maybe they've suddenly done a poo, in which case start over.
With my method of letting DDs have some peace when they were tired it meant the maximum they cried was 10 minutes, whereas if I'd continued to hold them, rock, coo etc they'd have been crying for far longer.
In the middle of the night if DDs cry I wait to see if they've just got unsettled and they usually go back to sleep. When they were still having night feeds then of course I fed them immediately. I let them decide when that was, although once I knew they could do without a feed they might have woken a few odd times crying and I waited for as long as I thought it might take them to get back to sleep before going to them if it seemed too long.
I'm not a big fan of the name CC as it seems to be used in a way that means letting your tired crying baby have some peace means they cry more than if you rock/hold them. From my experience and that of my friends I would say that giving a baby some peace and quiet once they'd worked themselves up and were tired leads to far less crying and faster getting to sleep than constantly rocking a crying tired baby.
Obviously if you've timed your day right there is no crying at all apart from waking in the night for a feed.