Eiffel Tower Ticket

Help! I've been trying to purchase a ticket on the official Eiffel Tower website for months, but it was too soon. My month of travel has not been available yet. I plan to visit the end of May, and the site is currently only showing dates through April. The month of April just opened recently, and the dates are all suddenly filled. I fear this will happen when May is released, and I don't know when that will occur. How do I purchase in advance? I can't seem to purchase yet for May, but I'm concerned that it will fill immediately upon opening. Is there another way to purchase in advance?