No, I've done that frozen thing with strawberries. This is the traditional Daiquiri AKA "the favorite drink of Ernest Hemingway":
"Always do sober what you said you'd do drunk. That will teach you to keep your mouth shut."
Sound advice from the Old Man.
3/4 oz Fresh Lime Juice (fresh is important)
1/4 oz simple syrup*
Add all 3 ingredients to a martini shake 1/2 full of ice
Strain into a chilled cocktail (martini) glass
This drink is almost good enough to forgive "Papa" Hemingway for this:
* Make your own at home. 2 parts sugar to one part water. Boil the water, add the sugar until fully dissolved, let it cool, then use it. Any extra will keep in the fridge for a while.