beefing up rear springs for towing, too much sway

What can I do, Install, in the rear suspension to stiffin it up? I bought a larger travel trailer, ( within tow capacity), use a sway bar but I still don't like the feel on the highway. It doesn't seem to do it towing with a truck with leaf spring but does with coils. Any thoughts?

What does it do? Sag, sway, wander?

if you have the cheaper rated tires you need to step it up to the more aggressive goodrich all terrain tires that load max 2500 lbs per tire. I used to have that problem with the michelums xlts. Too soft and not good for towing. My tires now hold 65psi air. I found that when you start to sway at 60 it will stableize by jerking the wheel left right from 8 to 10 a few times. Just get a bigger truck if this dont work. Mine is rated for 6200 tow capacity, not all tbs are rated for that.