Factory Stock Tower Braces
From the factory, Mustangs were equipped with two separate shock tower braces, left and right. These are an integral part of the body bracing to ensure structural integrity. Without these braces, the shock towers would tend to move inward and the car's handling ability is greatly reduced. These braces keep the basic chassis in shape. This technique was used throughout the first generation Mustang. The Competition Suspension option for 1970 used braces that had additional reinforcing plates welded underneath at the rearward mounting points. Ford also knew it helped things along to add a straight brace at the rear mounting bolts that connected the rear of the two shock tower braces. You will see these on Boss cars.
Note of Interest: For 1969 and 1970 Mustangs, there was only one part number for each side, left or right, even though some of the braces had the extra reinforcement for the Competition Suspension. Back in the 80's, a long time Ford parts counter man who I've known through the years told me that this caused some confusion because if someone wanted a replacement brace, he had to know if it was a reinforced piece or not and then he would just have to go back and look at all of the braces with that part number to see if any of them had the reinforced end. Just one of the many odd situations dealing with factory parts sometimes.
Shelby Type Export Brace
In 1965, Carroll Shelby installed a single piece brace called an Export Brace. These replaced the two separate braces with one brace that went from shock tower to firewall to shock tower with one thicker and stronger metal bracket. This one piece design was used on Mustangs that were destined for export to another country and were designed to help the chassis withstand the rigors of shipping overseas. Shelby liked the idea and used them on his GT 350's for better handling and stiffer roll control. All Shelby's came with this brace.

These export braces are available through just about any Mustang vendor and will substantially improve your mustangs handling. The difference in cornering will be felt immediately. You can always store your original braces for a time when you might want to put them back on. These export braces are a simple bolt on procedure.
Only two things need to be considered:
1. The original braces install over the upper shock mounts. These upper shock mounts install over the ends of the export brace. The original braces are removed first, then the upper shock mounts are removed. The export brace is installed first and then the upper shock mounts on top of the brace.
2. Even with the original braces in place, over the years the shock towers may have moved inward. This can make installation of the export brace a bit of a pain if they have moved too much. You may have to use a large pry bar to position the ends of the export brace so that the bolt holes will line up with the shock tower mounts. It may help to place a jack underneath the car under the engine cross bar and lift the car a bit and the shock towers will move outward a small amount. This may help you align the brace end bolt holes.

This is a very inexpensive modification that will dramatically improve the fun and handling of your Mustang..