Teeth can be moved vertically (up and down) into alignment. There is also a technique called enamelplasty that can be done to give the appearance of leveled teeth. However, when gum disease (periodontitis) is present, it is not advisable to move teeth orthodontically. I would recommend a visit to a periodontist (gum specialist), who will lead you in the right direction. If he/she ok's orthodontic treatment- you would be able to proceed.