Hi,
The more the muscle of an animal is exercised the longer the meat fibres, the greater the quantity of connective tissue developed, sinews ets and the longer the cooking time required.
When braising it is best not to use to large a pot. It is best if the fit is quite tight - by this I mean that you should be able to put the lid on the pot easily, but when it comes to turning the meat you should be thinking uumm - how am i going to do this - it`s going to take a few forks and a bit of care.
The meat should be browned/seared on all sides. Then place on a mirepoix or bed of vegetables. Typical vegetables for a beef, lamb, venison braise would include: carrot, onion, celery, garlic cloves . I use whole garlic cloves and then squeeze out and add to the juices to make the sauce. Seasonings can include bouquet garni for all meats, for venison, include a few juniper berries, a couple of whole cloves and a few strips of orange peel. Place the vegetables in the base of the pan, place the browned/seared meat on top, add stock, wine etc to make a layer of about 2 ins. cover and braise.
This can be done in an oven 180C/350F/Gas 4 or slightly lower.
A typical problem can be loss of cooking liquid - this has been known to fool many a student into thinking that the meat is cooked - not so!
Now I have to confess I know nothing about Dutch ovens, but I have braised various cut of meat for years and used to be a food lecturer. If in any doubt as to whether the pot has a good seal, it is possible to seal the pot hermetically by making a paste of flour and water and putting it around the rim before putting on the lid.
One further word on braising - I wouldn`t dream of doing a beef or venison braise without first marinading the meat in some red wine, splash of olive oil, garlic cloves (halved) sliced onion, sliced carrot, bayleaf, any spices as appropriate for at least 8 hours and preferably more.
Julia Child recommends 3 1/2 - 4 hours for a 5lb beef braise at 180C/350F/Gas 4.
My old teaching recipe says 1 1/2 - 2 hours for a 2-3lb piece of topside, rump or silverside.
I hope this helps and doesn`t cause any confusion.
All the best,
Archiduc