Squeeze the juice of 1/2 lemon into a medium bowl of cold water. Break off
stem of 1 artichoke and largest leaves at bottom. Put artichoke on its side
on board. Holding a very sharp knife or small serrated knife against side
of artichoke (parallel to leaves), cut lower circle of leaves off, up to
edge of artichoke heart; turn artichoke slightly after each cut. Rub cut
edges of artichoke with cut lemon. Cut off leaves under base. Trim base,
removing all dark green areas. Rub again with lemon. Cut off central cone
of leaves just above heart. Put artichoke in bowl of lemon water. Repeat
with remaining artichokes. Keep artichokes in lemon water until ready to
cook them.

To cook artichoke bottoms, squeeze any juice remaining in lemon into a
medium saucepan of boiling salted water. Add artichoke pieces. Cover and
simmer over low heat until tender when pierced with knife, 15 to 20
minutes. Cool to lukewarm in liquid. Using a teaspoon, scoop out hairlike
Choke from center of each artichoke.

Alternative: trim then pull each leaf; scrap to remove the choke.