Another thing that softens the rear wheels ride is a full tank of gas. i.e. - more weight in the rearend. When your gas tank is half full, it's time to refill gas tank to full again to maintain a softer ride. This is also prevent your fuel guage sensor from rusting, which will keep your fuel guage working accurately long term.
In an earlier post, I said 3 psi low tire pressure safely improves ride comfort. I actually meant front tires when I said 3 psi low is good. Now let's talk about rear tires.
Assuming your car has engine in front and is 2 wheel drive like mine is...
Run front tires 3 psi lower than specified on door frame sticker. Rear tires 6 psi low. Never let gas tank get less than half full. The more gas in tank the better for softer ride at rear tires. Those are free things I did on my Buick Park Ave, which helped ride quality a lot. For my Buick, I had 27 psi front tires, 24 psi rear tires before I bought Hankook All Season tires.
After buying Hankook All Season tires (which ride softer) I started keeping my front tires at full recommended 30 psi that's specified in door frame sticker. 30 psi front. 27 psi rear. Rides great, handles good, gets good gas mileage, no low tire pressure warnings.
If you have a front engine, 2 wheel drive, 1/2 to full tank gas, and aren't carrying heavy cargo in rear; then try front tires 3 psi low, rear tires 6 psi low.
Automatic low tire pressure sensor warning on dash is triggerend when one front tire and diagonally opposite rear tire are more than 3 psi different. At least that's how my Buick tire pressusure monitor works. So as long as I keep the front to rear psi difference to 3 psi (or less) I don't get tire pressure warnings on my dash nor warning bell alarm.
Also, my ABS works fine with a 3 psi difference front to rear.
If your car is front engine and works somewhat similar to mine, you can safely run front tires 3 psi low and rear tires 6 psi low with no problems and get a smoother ride. If you need to haul heavy cargo, add 1 psi per 100 lbs to rear tires up to a maximum of psi recommended on door frame.
For convienience, don't worry about adjusting rear tires psi for loads in trunk that are under 100 lbs.
Note: After lowering rear tires 3 psi lower than front tires... Reset your electronic tire pressure monitor (in the hope that it will remember and accept this psi configuration without setting off tire pressure warnings). I don't know if this is really necessary or helpful, but I did this for my Buick and I have no tire pressure warnings or problems (as long as the front to rear difference is within 3 psi).
I don't know if resetting your tire pressure monitor is necessary or not, but it can't hurt, might help it accept your new tire pressure configuration without it squawking.
If your tire pressure monitor still squawks (even after reserting it) about a 3 psi diiference beween front and rear tires, then try running rear tires only 2 psi lower than front tires (and reset tire tire pressure monitor again).
Notes and Warnings: My tire pressure advice to run rear tires lower psi than front tires is good advice only for front engine, 2 wheel drive cars. i.e. - front heavy, 2 wheel drive cars.
Do not follow the above advice in this post for rear engine cars.
Do NOT follow the above advice in this post for all wheel drive cars. If your car is all wheel drive you can run front and rear tires 3 psi low, but the front and rear tires psi must be same psi. i.e. - For all wheel drive cars, all tires need to have same psi.