  We prove several estimates for the volume, mean width, and the value of the
Wills functional of sections of convex bodies in John's position, as well as
for their polar bodies. These estimates extend some well-known results for
convex bodies in John's position to the case of lower-dimensional sections,
which had mainly been studied for the cube and the regular simplex. Some
estimates for centrally symmetric convex bodies in minimal surface area
position are also obtained.
