The first thing that jumps out at me: that rear tire does not belong there. It's 'way oversized, which reduces trail and makes the bike very choppy, both going into, and coming out of, turns. It raises the rear too much, reducing the trail up front. Go down on rear tire size, get a rounder profile. For real tight, solid twisty action, go to "V" profile both ends, use TT100 series tires or similar (never do this on just one end!). Sizes ("V" tires) should be about 4.50 to 5.10 rear, 4.10 front. Round profiles: 3.25-3.50 front, 4.00-4.25 rear (that's 100-115 front, 120-130 rear, in metrics)
Make sure the front end has tapered roller bearings, not those awful balls and races. Those things only last about 1 year or 5,000 miles before they start developing notches in the "straight ahead" position, which makes the bike kick back out of turns, right after you've laid it over.
Make sure the front fork oil is 10w or 10w30, no heavier. Teflon-based oils are best in the K0-K3 front ends. Add at least 1/4" to 1/2" spacers inside the front fork tubes to bristle up the front springs, which are sagged from age, now. Make sure the front forks are properly aligned, for smooth action. If the seals are leaking, find the teflon-coated version of the seals and use them.
The rear: use shocks in the length range of 12.75" to 13.125". Longer, if you weigh more than 150 lbs., otherwise, shorter. Stock length is 13.06". Spring rate for spirited 1-up riding should be 110 lbs/inch, unless you weigh more than 170 lbs, then consider 120 lb. springs. Progressive springs can be 90/120 if run with 3-5 notch preload and you are a lightweight, otherwise look into 100/130 lb units. Progressives let you "lighten it up" if going on a long, easy ride and don't feel like pounding along: drop a couple of notches for those rides.
Swingarm: make dead sure the bearings are tight and the arm moves freely up and down, with NO side-to-side movement. If you can move the rear wheel side-to-side, while the bike sits straight up on its wheels (someone else holds it up for you), and you flex the rear wheel side-to-side within the frame: the bushings are bad. If you can, for example, move the wheel 1/16", the bike can move it three times that much in a turn. (I can rebuild those to race quality for you for a nominal fee).
Tire pressures: typically the front ranges from 32 to 45 PSI, depending on tire type. The rear can range from 32 to 48 PSI, also depending on load and tire type and size. A rule-of-thumb: on a 70-90 degree day, measure the tires cold, then run at speed for at least 10 miles, then stop and quickly measure the tire pressures again. If they rise more than 2 PSI, you don't have enough beginning pressure. If they rise 2 PSI, you're on the money. If they rise 1 PSI or less, they are either overinflated or too big for the loads.
Finally: don't overlook the engine mounting bolts. These are too often loose, and are part of the anti-flex structure of these frames. On mine, I have doubled the mounting plates at the front and upper rear, where they attached the engine to the frame's bolts. This helps, too. Make sure your chain and sprockets are in good condition, because these can cause "snatch" when entering and leaving turns, or changing gears or thrust rates (i.e., throttle settings) in corners. The chain/sprockets must be very smooth, and WELL lubed. Forget O-ring chains, if you're looking for smooth corners, and use Honda's own sprockets. There's a big difference with those (you can find my comments about this in "Thoughts of Hondaman" in the FAQ).
My never-do-without tips on my own bike, even now (based on my roadracing days):
1. Check the steering head bearing tightness every month.
2. Grease and check the swingarm bushings every 3 months. Use only oilite bronze bushings, clearance less than .001".
3. Clean and lube the chain weekly (if daily ridden). Set at 3/4" slack.
4. Rear shocks: 12.875" long, run 2nd notch for commuting, 3rd for Rocky Mountain 1-up riding, 4th for me and her together.
5. Front (3.25) tire: 38 PSI. Rear (4.00) tire: 38 PSI me, 40-42 PSI 2-up.
6. New wheel bearings if EVER any looseness shows up. They're cheap!
7. Check wheel alignment after every chain adjustment. My "straight" frame setup is 1/3 notch forward on the right side, as compared to the left. This is more common than you might think: Honda wasn't particularly accurate about drilling the swingarm bolt holes in the K0-K4 frames, and one side being off by .04" (which is their spec) offsets the rear wheel by 1/2 "chain adjuster" notch back at the rear axle. (Sad, but true). By the time the late K4 cmae along, the frame jigs were much "tighter".
With stock tires (3.25 front, 4.00 rear, 13.06" long shocks), the front trail is 3.75". This is a little short for hotrod cornering, but makes the bike feel lighter in tight city driving. A 4.00" trail is better for entering and leaving corners at 50+ MPH, by a very noticeable amount. Lowering the rear, while raising the front (each a little), will get you there.
One last thing, some call "controversial", but I call "can't live without": air forks up front. Easy to install (search the forums). Don't run more than 10 PSI up there, though.
