Suddenly Swaying

I changed from mostly worn down Michelin LTX MS2 tires in size 245/75R16 LRE last year, which were incredibly stable, to Cooper Discover AT/3 tires this year in size 265/65R18 LRE. I definitely notice more tread squirm, but they did improve after towing a bit. We took a 2000 mile trip and I was still happy with them, the steering is not as precise as before on the highway but felt pretty stable by the end of the trip. I noticed improvement in just the first day of driving (250 miles?). The Michelin's, once worn down a little, had a solid rib of rubber along both shoulders of the tire. The Cooper tires have full depth tread blocks, even on the shoulders so the increase in squirm was somewhat expected. I've used this tire before on my dad's truck when they were nearly worn out and they were great then. They will improve over time. The good news is they work much better when not on the pavement, I wanted a slightly more aggressive tread and am not disappointed. If I was never going to go off pavement, I'd have stuck with an all season tire with a more stable tread.