Answer:
   
   The requirement is that it be done at the eighth day. The Rambam (just
   beyond the section previously quoted) says that earlier the baby is
   too tender and later the father might not be able to bring himself to
   do it. Some doctors have said that after, the baby develops too much
   and would actually be a more serious matter.
   
   With adults, the question is different. After the eighth day the
   nervous system becomes more developed (especially after puberty). For
   adults, a local anesthetic is used (often a mixture of lidocain and
   prilocaine). It is spread on the area, some time is allowed to pass,
   and the procedure is performed with no pain.