Best Lemonade

This is from Cook's Illustrated, the magazine that was the source of the "Best Recipe" cookbook I like so much.  This is very similar to the way I've always made lemonade except for the part about mashing the lemon slices with sugar.  The description of the recipe made it sound like that step makes a huge difference.  I can't wait to try it.  I've always added a little salt (about 1/2 tsp to 1 tsp) to my lemonade also, which this omits.

 Look for large, slightly soft lemons—they tend to be extra-juicy. Store the lemonade in a covered container in the refrigerator for up to 3 days.  

1 large lemon , sliced thin, ends discarded 
1 1/2 cups sugar  
7 cups cold water  
2 cups fresh lemon juice (from about 12 lemons) 
 Ice (for serving) 

Using potato masher, mash lemon slices and sugar in deep bowl until slices release their juice and sugar begins to dissolve. Stir in water and lemon juice until sugar completely dissolves. Strain out lemon slices and chill or pour over ice before serving.