I always ran Cooper Discovery on my of F 150 and loved them. They MAY be a little loose feeling when you first put them on but once they get any wear on them at all they are excellent towing tires. They may feel loose due to deep tread and the tread pattern they have but that's not uncommon for anyone putting 10 ply tires on for the first time. On my truck I noticed it more when NOT towing than when the trailer was hitched up.
Good luck / Skip
2011 F-150 HD Ecoboost 3.5 V6. 2550 payload, 17,100 GCVWR -
2004 F-150 HD (Traded after 80,000 towing miles)
2007 Rockwood 8314SS 34' travel trailer
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