Photo from Bogdan Suditu's photostream
It is always a challenge to keep homemade pickles crisp, but it is a lot easier with fermented pickles that are never cooked. Even in fermented pickles, there is some slight decomposition due to fermentation, and adding some tannins helps keep pickles crisp. Many plant leaves, such as oak, contain tannins. You could use white oak leaves but they are so high in tannins that you probably could not eat the pickles for the pucker!
Red Currants photo from guldfisken's photostream
Some better options:
Horseradish leaves and/or peeled and chopped roots
Black or Red currant leaves
Red raspberry leaves
Raspberry photo from Zaggy J.'s photostream
Some home brewers use organic green or black tea leaves in brewing beer to provide tannins (which give body to the beer). I don't see why that wouldn't work in keeping fermenting vegetables crunchy, but I haven't read of anyone doing it. Of course, we are just now re-discovering the benefits of fermented veggies, and surely many of the tips and techniques were lost when our grandparents' generation stopped making them. I read somewhere that wild greens like purslane also help keep pickles crisp but I cannot find the reference again.
Salt also hardens the pectins in vegetables, making them crunchier. (Plus, salt inhibits the growth of bacteria [other than lactobacilli] and extends storage time.) However, there is a fine line with the amount of salt used for preservation so it works, and yet the vegetables aren't so salty you cannot eat them even with rinsing. I think it takes an individual 'trial and error' to find the right amount of salt you prefer.
Another tip: Every type of fruit/vegetable has enzymes whose purpose is to break down the food to make it decompose... the whole point of food from a growth standpoint is to make seeds, then decompose so the seeds will grow. Most of those enzymes are concentrated in the blossom end (not the stem end) and by cutting a bit off the blossom end, you discard a lot of those enzymes and help keep your dill pickles from getting mushy.
Here's a recap with links to the recent posts on fermented vegetables:
Eating Lacto-Fermented Vegetables
Science and Hysteria in Lacto-Fermenting
Crock Fermented Garlic Dills
Fido Jar Fermenting Basics
Fermenting in Ball Canning Jars
Keeping Pickles Crisp
Pickles, Lacto- Fermentation or Old-Time Fermentation
Preserved Grape Leaves