There are certainly advantages of delayed cord clamping, the main one being that the baby recieves more red blood cells which can prevent anemia in the newborn phase and also later into infancy and toddlerhood. The reason delayed cord clamping is not "standard" practice is because there is no clear evidence as to whether it is beneficial enough to recommend for all births. One of the concerns of delaying cord clamping is causing jaundice - all newborns have more RBC (red blood cells) than what they actually require after birth, these RBC's have a shorter lifespan and the liver (which processes dead RBC's) is still immature. So the concern is that giving the baby MORE RBC's through delayed cord clamping will increase levels of jaundice. Now that said, most babies have some degree of jaundice but if the levels are too high, they require phototherapy in special care nursery because jaundice can cause toxicity leading to brain damage if left untreated. Phototherapy is pretty main stream, but it does mean being seperated from your baby and extends your stay in hospital and often also requires IV fluid therapy or early introduction of supplemental formula. Of course, not every baby who has delayed CC will go through this and certainly lots of babies who do have the CC immediately will still end up going through this, it's simply something to be mindful of in making your decision. You have to weigh this risk up with the possible benefit of more iron stores - which in developed country such as ours where food is readily available, is it really vital that the baby has a higher iron store? Maybe, maybe not. Personally, I probably will delay cord clamping for my next baby, but will do so fully informed.
As for managed third stage, I think that is a personal preference but the main risk of not having the injection is that it increases chances of large post partum blood loss. But you can always specificy that you are happy to have injection in the event that bleeding is significant or if the placenta is taking too long to detach
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