For special contstructions, it is difficult to obtain full coverage. Almost all companies have certain requirements. Turn signals, stock rake, no stretch, front and rear brakes, dual throttle, no open primary etc..... So for a stock looking special construction, it would be easier, but who builds a stock bike?
You have to put yourself in the insurance companies shoes: Someone has a radical frame, long front end, no front brake, no signals, minimal lights, a meat grinder primary, and they say it's worth 17 grand.
So, the suit at the insurance company is worried, you'll wreck, and they have to pay you 17 grand, or someone steals it and they have to pay you 17 grand. Or you and your buddies take it all apart and you report it stolen and they have to pay you 17 grand.
So special constructions are a huge risk for them, and therefore if you can jump thru all the hoops and get the insurance, your going to pay the price for the risk they are taking.
So alot of guys want full coverage, but either decide the price is too high, or there bike doesn't qualify for it, so they have liabillity only. It also depends on your location. I had to shop around for full coverage, I couldn't get it from Geico or Progressive like others said in this thread
Sixball