Perhaps your embroidery machine has a built in alphabet. It is a problem as most alphabets are just too large, and can't be sized down without getting too dense.
Jolson Designs has some that are 0.5 inches.
http://www.jolsonsdesigns.com/ser...
http://www.jolsonsdesigns.com/ser...
http://www.jolsonsdesigns.com/ser...
have a look at 'Brush Script' on the EmbroideryDesigns.com web site.
You might look at apex embroidery. They have lots of different styles and sizes of fonts. A stitch a half has the chicago style, but it is not script. Chicago measures .37 x .65. Then sewforum has the hemi alpha that measures .42 x .67. I don't remember what style it is. The last place I have a small one from is sticharymall with one named fanciful that measures .89 x .68. It is script style. Most of these are free or very low priced. Hope this helps.
There has been a tiny alpha at Skeldale House available to members of her group and another very small one at Yummy Factory, recommended to use to embroider around the binding on baby blankets.
I think I remember getting one on Designs by Sick once, a long time ago. Maybe it was called "Tiny Font" or something like that? I'm sure someone will know of others as well. Good luck with your search. Hugs, Marji