The smallest of all the place spoons, the Demitasse Spoon has perhaps served its better days. Few people even know what a demitasse is, they only know the "espresso" they order from Starbucks. And, the last time I was in Starbucks they did not offer me a sterling silver spoon to stir my espresso with.
Demitasse spoons were for (and still are for) times when we have the moment to sit and chat over a good cup of espresso. So those tee tiny little spoons you found at the bottom of your grandmother's silver chest were not part of a child's tea set, she used them when she served espresso to her guests. (Regular coffee would have been served with Four O'Clock or Five O'clock spoons.)
The pictures do not do the pieces justice. They are so much smaller, that it is amazing (at least to me) how the companies just miniaturized the details of the pattern.
Etruscan by Gorham (4 1/4 inches)
Old Colonial by Towle (3 7/8 inches)
Louis XV by Durgin (4 inches)
Poppy by Gorham (3 3/4 inches)