Writing Exercise: Creating Dialogue for a Laconic Character

A while ago, I posted some writing advice from other writers and my professors, but sometimes I have ideas of my own.

One possibly interesting excercise: Write a laconic character.
His/her dialogue would cut out *all* unnecessary words. This is not something I've done yet, personally.

One way to do it: Write his or her dialogue as whole sentences, then go back and heavily edit those sentences down to a handful of words. For me (though not necessarily for others) this might be the easiest way. Whole sentences come more easily to me than one-word snippets. I wonder if a laconic character would always speak in whole sentences--in those one-word statements that are already accepted as proper statements in English--or if he/she would be a bit more eccentric and take out any and all redundant words and say only the worlds that will get his/her point across, proper grammar be damned.