There could be a lot more to it than that. It depends on the type of cookie you are making and what you mean by delicate. Different flours have different levels of protein in them. You may even need to look into cake flours or part rice flour to change the texture of your cookie. Cooks Illustrated is a great source for this type of information.
This is the basic recipe I use when I want a delicate texture. I either ice the cookies after cooking or wedge two together with cream fillings. 185g butter, 1/2 cup sugar, 2 eggs, 2 cups self raising flour, 1/2 cup custard powder. Cream butter and sugar until light and fluffy. Beat in eggs, one at a time. Gradually fold in sifted flour and custard powder. Put teaspoonfuls on baking tray and press down lightly with floured fork. Bake at 180C for 10-15 mins until golden. This is a really nice cookie.
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