The timing of enrollment changes does not matter, as long as you enroll before the Medicare Open Enrollment period ends on December 7. Keep in mind that it can take some time to compare plans, and you may want to have a list of all the medications you take and the providers you see before you sit down to compare plans. If you wait until the end of the Medicare Open Enrollment period to enroll in a plan, you should still receive your new plan information before your new coverage takes effect on January 1.