Interproximal reduction (IPR), stripping, slenderization, or enamelplasty is always one of the biggest concerns of Invisalign patients. This procedure is not limited to Invisalign but also used with patients in fixed braces.
Recently, in the American Journal of Orthodontics and Dentofacial Orthopedics, Zachrisson, one of the most famous orthodontists of our time, published a paper showing the stability and safety of this procedure after 10 years of study. The key is the proper technique of reduction. Sheridan has described the proper protocol for high speed reduction (HSR).
In some cases, IPR may actually produce a more aesthetic result since it may improve the contact between teeth and eliminate "black triangles" caused by some recession of the interdental papillae (the v-shaped gum between teeth). It may be required to relieve crowding, when expansion and proclination of teeth is not desired.
Proper radiographs may be required to determine the amount of enamel possible.
*From a personal standpoint, I have undergone this procedure myself and had no adverse problems.