THE IDEAL RIBBON for folding is Petersham, named for a British officer of the late 18th century. It's used by tailors for waistbands and by milliners for hatbands because of its flexibility. However, some grosgrains can work just as well. A grosgrain with a jagged or saw-tooth texture on one side will fold well.
If these aren't available, look for fold-friendly ribbons containing at least 50% cotton. The cotton provides some give when folding. If the fiber content isn't given, test a piece of ribbon with an iron. With the ribbon flat on an ironing surface, bend the ribbon into an arc and steam-press it to check its flexibility. If it holds the curve, the folding will go more smoothly.
Press the ribbon before starting to work.
When folding ribbons together to create a straight strip, frequently check the ribbon's position to keep the sides even and parallel.
Use a large paper clamp or clothespin for a "third hand" as the folds increase. Clamp the finished folds to keep them in place.
Watch your tension, and keep it consistent. A stressful day may mean tighter folds.
Select ribbon that has some body. Lightweight ribbons won't hold a fold well.
If decorative ribbon selections are limited, try making your own. Select a wider ribbon as your base. Next add one or two coordinating ribbon(s) down the center, or along each edge of the base ribbon, and machine stitch in place with a matching thread.
Wired ribbon can be used, but first remove the wire for easier folding.
Sources
The following companies offer a wide selection of ribbon and ribbonry books.