Beat the butter with an electric mixer until creamy. Gradually add the granulated sugar and beat until mixture is fluffy, about one minute. Add the eggs, cream of tartar, baking soda, vanilla and salt, and beat until combined. Gradually add the flour, 1/2 cup at a time, beating well after each addition, stopping as needed to scrape the sides of the bowl with a spatula. Stir in the fruit slice candies. Cover and chill for 2-3 hours, until mixture is very firm. (If you are in a hurry, you can alternatively place the dough in the freezer for a half hour, allowing it to sit out for 10 minutes or so before proceeding with the next step.)

Shape dough into 1-inch balls, and roll each ball in the sugar crystals. Place cookies on greased cookie sheets, and bake at 375 for 8 minutes. (Do not overbake; cookies will appear quite soft when you remove them from the oven, but they will firm up as they cool.) Cool on a wire rack.