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A fresh artichoke will be quite heavy and deep green.  The artichoke should also have tight leaves that make a squeaking sound when squeezed together. The leaves should not look dry or split apart.  Smaller artichokes tend to be more tender, but large artichokes have larger hearts, and the hearts are generally the sweetest, most flavorful part of the vegetable. Rinse well under cool, running water and pat dry with clean paper towels.  Artichokes tend to hold a considerable amount of dirt and debris inside the tips of the leaves, so you should gently scrub the artichoke with your fingers as you rinse it to dislodge most of the dirt. You can also let the artichoke soak briefly in a bowl of cool water for a few minutes before rinsing it, but this is not strictly necessary. Rinsing is usually a sufficient way to clean an artichoke. Do not wash artichokes before storing them since doing so could cause them to spoil faster. Wait until immediately before you plan to steam the vegetable. . Use a sharp knife to cut off all but 1 inch (2.5 cm) of the stem.  You could cut the stem off completely if you plant to serve the artichokes upright. Artichoke stems are edible, but they tend to be bitter, so many people prefer not to eat them. Use your fingers to strip the bottom leaves from the artichoke.  You should be able to remove them with your fingers, but if you have a hard time, cut the leaves away with a knife or scissors. You only need to remove the small, fibrous leaves from the very bottom of the artichoke. You do not need to remove the outer leaves along the side. Hold the artichoke on its side with one hand and use your other hand to cut off 1 inch (2.5 cm) of the pointed top with a sharp knife. This step is not strictly necessary, but removing the tip can make the artichokes safer and easier to eat. Use sharp kitchen scissors to snip off the prickly tips from the remaining outer leaves along the sides. The leaves themselves are good to eat, but these prickly portions can scrape your mouth and taste unpleasant. Rub one-half of a cut lemon over all the cut edges of each artichoke. Artichokes are prone to oxidation and browning once cut. Acids, like lemon juice, slow the oxidation process long enough for you to cook and serve the artichoke.

Summary:
Choose good artichokes. Wash the artichokes. Slice off the stems Remove the outer leaves. Cut off the top, if desired. Trim the remaining leaf tips. Treat with lemon.