If you have learned how to use a roux properly, you should be able to make a smooth, lump-free sauce. However, to bring a sauce's texture to perfection, to create the velvety smoothness that is important to a good sauce, straining is necessary. Even a slight grain-iness that you can't see can still be felt on your tongue.
Straining through a china cap lined with several layers of cheesecloth is effective. Very fine sieves are also available for straining sauces. Straining is usually done before final seasoning.
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