Firstly I'll explain what I think each method means from the research I have as I think so many people do not understand what CC/CIO involve.
CIO -
Setting times for LO to sleep and nap. At designated sleep time a pre-nap/bedtime routine is done and baby is put into cot fully awake. Parents leave room. Checks are limited to every 20mins with the minimum of reassurance to allow baby to self-settle without any help. At end of designated sleep time LO is taken out of cot even if hasn't fallen asleep yet.
^ This is the method that I don't agree with. However, I have NEVER met nor heard of any person doing it this way. When most people say they think CIO is awful I think that they only think of this method and people can get confused as some people use the term CIO to describe CC (below).
CC - Controlled Crying
When baby is ready for a sleep or nap a pre-nap routine should be done in the dark+quiet sleep area. Baby should be cuddled and put into cot calm and drowsy but still awake. Baby shouldn't be given any props such as a dummy/pacifier (as then CC is pointless as they still rely on having the prop to get to sleep so will still wake for assistance) but can be given a small safe comfort blanket or toy. White noise or swaddling may be used to comfort baby however bear in mind that if you want to wean baby off of these when they are older you may need to do another 1 or 2 nights of CC again. Although generally I've found that once a baby has become a good sleeper it's fairly easy to take these things away!
Baby can be soothed in cot when put down and should be left completely calm and happy. A cot mobile or lightshow could be started when parents leave the room.
Parents should stay outside the room is listen on a monitor so they can listen to babies cries. It helps if both parents (or someone else to help) are there to take turns as this will be the hardest and most devastating thing you have ever done.
When baby starts to cry parents should wait a certain amount of time. The books and websites I have read all suggest different times. The shorter the time intervals the longer it will take CC to work but you might prefer it to be a bit gentler this way. I would suggest on the first night going in after 1 minutes then after 3minutes then after 5minutes then after 8mins, 11mins, 15mins, 20mins (never any longer). I can guarantee that if done correctly with a proper wind down routine and reassurance your LO will not cry for the full periods between checks and will most likely fuss, moan, cry back to fussing etc. Don't wait any longer than you feel comfortable doing between checks.
When you go in you can comfort baby as much as you like. Cuddling, shhhshing etc. but don't do anything to help your baby fall asleep and always put them back down as soon as they are calm, fully awake. When you put them back down soothe them again so that they are as calm as possible when you leave.
For night wakings if it's been 4hours or more you should feed baby (if they are used to night feeds) but make sure to put down fully awake and use CC if necessary to help them fall asleep. They will drop the night feed on their own when they no longer need it as they will no longer associate feeding with falling asleep.
The second method is the one I used with my LO.
I didn't do it because I wanted to teach her to self-settle or because I fancied a full nights sleep or I wanted her to nap at set-times or because I couldn't be bothered rocking or holding her to sleep.
My LO did not know how to sleep. Probably a result of the terrible sleep habits we managed to create when she was tiny due to reflux and colic (she's fine now). I tried everything -
Co-sleeping, feeding to sleep, rocking to sleep, swaddling and white noise in swing, wearing in a sling, going long walks, lullabies, light shows, chamomile, lavendar, baby massage. I even bought an automatic pushchair rocker.
These methods would all help my LO to fall asleep but she could not stay asleep. The slightest change in anything would cause her to wake and start screaming because she was exhausted. During the day she would last around 10-15mins in a sleep before she realised that something had changed and she could no longer sleep. I could rock her to sleep but the only way she could sleep was in a pitch black silent room. So I would go into the room and have to rock her and the instant I stopped or slowed down the rocking because I was exhausted she would waken screaming. At 5ft2 and 96pounds I physically could not rock her for the whole of a 1hour30minute nap she needed at least.
There was nothing wrong with her except she was extremely sleep deprived. She couldn't be put down from my arms for even a second without screaming. She was just so upset and frazzled all the time. If anyone else tried to pick her up or speak to her she'd have a meltdown because she was permanently upset.
She did sleep better at night but had several night wakings and was still not fully refreshed when she woke in the morning, getting progressively worse as the day went on. I was exhausted and used to sob as I tried to get her to sleep as I knew I had no choice but it was pointless as she'd just waken and scream anyway.
Shorty before 7months I decided I'd had enough and did CC. Best decision of my life. The first night/day was horrendous. It was so hard I would shake and vomit with having to listen to her cry - it goes against every bone in your body. After the 2nd night she slept through and I knew there was no going back ever. Naps took a little longer - about 3-6 days to completely fix. And the end result - a happier, more rested, more productive baby. She's literally transformed - She goes to bed at 7pm after her snuggles with Mummy and Daddy and she laughs at us as we give her a kiss and say night night. We give her a cuddly teddy and put her slumber bear noise on and start her mobile. She kicks and plays while watching her mobile and we leave the room. When the mobile stops we hear her yawning and shifting about to get comfy and then we don't hear a peep all night. In the morning she wakes up and we hear her shouting (usually Da Da Da) and "talking" to her teddy.
We go into the room and she greets us, completely refreshed and happy with a huge smile and lifts her arms for us to lift her out of the cot. We go into the living room for our morning wake-up snuggles then we get her changed for the day. She then has her milk and breakfast and comes to "help" while I get dressed, tidy up etc. Then we play silly games until she starts to yawn and I know she wants to go to bed for a nap - we go into her room for a cuddle and I put her down and repeat the same as at bedtime. And then she wakes up happy and refreshed again. Terrible parents????? No I don't think so.
discusting, but quaranteed to keep our LO's quiet I imagine........ 
. I don't agree that all babies need sleep training to sleep properly; with all of mine I have gradually moved from co-sleeping to putting them in their own bed asleep, then their own bed when half asleep, then their own bed when fully awake and they have learned to self settle with no need for crying or constantly having to go in every few minutes to reassure them. xx
