There is a great recipe in the book "The Joy of Pickling" by Linda Ziedrich but we are in the midst of a house renovation and I can not find my copy. I have made these on several occasions and they always turned out good.

If you are still interested I found the recipe. Do a search on Yahoo for "joy of cooking half sour pickles" The very first link is the pickle recipe.
The idea sounded so good I bought cukes at the farmers market and will be starting some today.

Here's a recipe from the harvest forum. Ken has been making pickles for many years.

Ken's Half-Sour Pickles
Source: ksrogers, Harvest Forum

5 1/2 ounces by weight Kosher salt
per gallon of room-temp water
--
Cloves of garlic coarsely chopped
Fresh dill heads
Fresh dill sprigs
Peppercorns
--
Pickling cucumbers - the freshest you can get

Use only very fresh water from the cold water tap. Measure Kosher salt by weight and thoroughly dissolve in water.
Put as many of the seasonings as suits your taste in the bottom of sterilized jars -- quarts, half gallon, whatever.
Pick, rinse, clean and cut 1/8" off both ends of cukes and pack tightly in the jars to about 1 inch from top. All cukes should be wedged firmly to stay under brine.
Pour the room-temp salt water brine over cukes and spices to 1/2" from top. Top with a new flat and a Ball Plastic Jar cover.
Flip the filled and capped jars over a few times to loosen and release any trapped air bubbles.
Return to upright position and then give the jars a "quick twist" a couple of times a day.
Leave on the counter for two days to start it working. (You probably will not see bubbles.) After 48 hours, open a jar, check the liquid level and adjust if necessary. If you wish, taste one of the top cukes, it will probably taste slightly of dill and salt. Remember it is not yet half sour.
If cukes are not mushy, bland or bitter, you have the option of adding a bit of salt or more water.
Reseal and leave on counter one to three more days. Taste sample again and if you are happy with the taste, add a tablespoon of white vinegar to each half gallon jar to slow/stop fermentation. (Adjust measure for the size jar used) Recap and flip over several times to distribute vinegar.
Place in refrigerator for a few days. Then you can start eating and keep eating up to a year (if they last that long).
IMPORTANT: If at any point in this process the brine becomes very cloudy or forms a scum, something is wrong. Stop, toss and start over.