In answer to the OP. I always found that bubs learnt to resettle in time. I personally hated the resettle concept, so I would just get bub back up when she awoke. At 4 months it is common for babies to regress in sleep a little bit and to have shorter and shorter naps, until they consolidate into less naps, but for longer (does that make sense?)

By 5.5 months we were down to 2 x 2 hour naps, and now we're in the process of those getting shorter and shorter, until I imagine she will be having one nap by 1.

As for letting her cry a little for 5 mins. It depends on the day for me. Some days if she's really fussing in my arms, I put her into the cot, and often she will stop crying, or just whinge off to sleep. At 4 months though she would often grizzle for about 5 mins before going off to sleep.

I was lucky though that DD had a clear "I want to sleep" whinge which was very different from "I need mummy" cry.

As for CC and CIO. I think they contradict my maternal instinct. I can't listen to crying without feeling physically ill. But if you're desperate, I think try anything that works for you.