If you are fitting a jointed bit, like a D-ring or loose ring snaffle, there may be no wrinkle on the lips at all. That doesn't mean the bit doesn't fit. Take a look inside the horse’s mouth by lifting the lips and notice where the bit is sitting on the bars. It should not be sitting so high or low as to hit the teeth on either sides of the bar. Pay attention to the horse’s reaction too. You horse might tell you by chewing and mouthing the bit, or other behavior, that it’s not comfortable. If the bit isn't positioned in the mouth evenly, the horse could start carrying its head to one side or toss its head. Adjust the bridle so the bit sits balanced on both sides and sits comfortably in the center of the bars.
Fitting the bit might not just be a matter of positioning, but of the size and shape of the bit itself. Horses can have differently shaped mouths, meaning different bits may be more comfortable for some than others. You might have measured your horse’s mouth and decided to buy a 5 inch bit. But the length of the mouth piece is not the only thing to consider. Horse’s mouths come in different sizes and shapes. Just like both my daughter and I have size 10 feet, that doesn't mean we like to wear the same shoes. Measure the length of our feet and we look like same size. But her feet are flat, while I have high arches. She loves her zip up jodpher boots, but I have to have lace ups. We don’t like to wear each other’s boots.
For example: you might think of a very thick eggbutt snaffle as a very soft comfortable bit, but for a horse with a fleshy tongue and low palate it may be an uncomfortable mouthful. So if you’re having trouble getting your horse to carry a bit quietly, consider trying another type of mouthpiece. Some horses like jointed mouthpieces, or seem more comfortable in different types of joints, such as a French link rather than a loose ring snaffle. Some horses may be happier with a bit with a port that gives some room for their tongue.
It can take a bit of trial and error to find the correct position in the horse's mouth for the bit. Try adjusting the bit according to the where the bit is sitting in the horse's mouth, and try different types of mouthpieces as well.