Higher air pressure = less bouncy ride?
Passenger tires, which are normally what is installed on people-haulers, are built for comfort and have thinner sidewalls and softer compounds. As a trade off you can get a mushy ride and when cornering, can feel very soft so you inflate the air pressure to compensate for this. This is also why the max pressure on the tire is lower since they're not really meant for carrying heavy loads but for more people-comfort so they're not designed for 'big' weights. You will also notice a bulge in the sidewall under normal pressures which can get cut easier if you stress the tire off-road or over rough terrain. What the manufacturer recommends for tire inflation is just that, a recommendation. Tires can be adjusted for ride and load which is why you can put more air in a passenger tire than recommended and still get a good ride out if it. This also depends on the size of the wheel and the amount of sidewall which is why car manufacturers go to larger wheels and low profile tires. It gives the option of running a softer 'passenger' tire with a smaller sidewall which decreases the 'mushy' feeling of the drive and makes the driving characteristics of the vehicle better.
Load bearing tires like D's and E's have thicker compounds, more belts and can withstand higher loads. They also have less flex and can cause very rough riding. These are normally 'truck tires' although many put them on smaller vehicles like Jeeps. Since the heavier tire causes the small vehicle to ride like crap, they will deflate them so it will ride softer. For example, I had E rated tires on my Rubicon when I first got it and it was a horrible ride. Even though the tires were rated for 80 PSI and the door sticker on the Jeep recommended 37 PSI, they rode the best at 25 PSI and still provided the thicker, heavier construction for off-roading over stones and sharp objects that would puncture passenger tires. Also, since they were a heavier designed tire, running at 25 PSI didn't cause 'mushy' driving characteristics. I've now gone back to stock p-tires but even though the recommended tire pressure is 37 PSI, I run 32 PSI since the Jeep is so light.
If you stick with factory design, stick with factory specs and generally you'll be good. When you start deviating you have to use a bit of 'redneck science' such as in the "tire chalk test".
