If you have overcrowding is it always neccessary to have teeth removed when having braces??

I went to to the orthodontist the other day for a consultation about having braces (I am an adult by the way). The orthodontist said I am suitable for treatment. The reason I am having orthodontic treatment is because I have overcrowding of the 4 front upper teeth. My two front teeth are situated in front of my other teeth (they do not protrude however). The rest of my teeth however are not overcrowded, and are in a straight line. However my orthodontist said I don't need to have any teeth removed because there is enough room for the teeth to be corrected into their correct position. But I don't see how the front 4 teeth can be moved without my other teeth being moved back slightly. Because my wisdom teeth have come through, there is no more room in my mouth for the teeth to move back without some being removed. Is it possible to have teeth moved without removal of other teeth?