A packer that is usable with a well includes a tubular inner core and a swellable body that is mounted to the core and is adapted to swell in the presence of a triggering agent to form an annular seal in the well. The swellable body longitudinally extends between first and second ends of the body and includes a first region that is located between the first and second ends of the swellable body to swell at a first rate and at least a second region that is located closer to one of the first and second ends than the first region to swell at a second rate less than the first rate.