x frame

The only "X" brace I'm aware of is for the convertibles, and it bolts up underneath the body, to help strengthen the body and keep it from flexing. They can be used on coupes, also, but do require some hole drilling on the earlier cars.
The top brace bolts up in place of your targa top to do the same thing...to strengthen the body with the targa top off.

That targa truss kind of just turns the coupe into a T-top!  That's pretty neat - but do you it's necessary for a daily driver or more for a racer style?  With that bottom X-brace, Corvette Central has a helpful step by step picture guide for install.  http://tech.corvettecentral.com/2012/12/1984-96-corvette-chassis-reinforcement/  looks to be a bit of work, but doable.  It also looks like a great idea but only needed on your coupe if you run with targa top off all the time?

I've read in several places that sometime in the '86 or '87 timeframe the factory strengthened the chassis to take care of the convertible twist and the coupe was based on the same upgrade. I always wondered if they meant that to be the addition of the X brace or did they do away with that for a truly stronger base frame.

Another issue with the bottom "X" brace is trans service accessibility....You have to un-bolt/remove the brace to get the pan off of the transmission.....

Most people know about the x-brace enhancement. What some don't know is that the rear bulkhead behind the seats, and cowl panels are also strengthened on the convertible. I owned an 88 convertible for several years concurrently with the 85 I bought new, and still own. The 88 was superior to the 85 in handling and road-feel. Much of the difference I attribute to the 17" 275's on the 88, but some of it was indeed the structural enhancements on the convertible.

I believe the x-brace was included with Z07 on coupes, but I've never confirmed this by observation.
I've flat-spun my 85 on two occassions under conditions that it should not have spun. The common denominator with the spins was the roof was removed. Chassis performance is indeed compromised when the roof comes off. The car won't achieve the same performance with the roof panel removed as it will with it bolted in place. There's a reason its bolted, and not latched with "quick release" latches. The forces transmitted through the top when driven near the limits of tire adhesion are too extreme for "latches". That's from Dave McClellan.