Dumb question - how to fork in a shell script

If a program calls a shell script, how can the shell script execute another
shell script in the background, in such a way that the second script will
keep executing after the first one exits? I tried just appending an
ampersand, but it seems like the second script is being killed as soon
as the first one exits. I thought maybe exec does this, but the bash
man page says that "exec command" causes the command to replace the
shell as the current process, rather than to start a new process. I
need it to actually fork instead.

The context is that I'm trying to get vgetty to convert the .rmd files
(some weird sound format) into .wav files as it receives them, but that
causes vgetty to block until this conversion process is done, and it
can't answer the phone again until it's done. The conversion should be
a background process.

-- 
  _______                   Shawn T. Rutledge / KB7PWD  ecloud@bigfoot.com
 (_  | |_)          http://www.bigfoot.com/~ecloud  kb7pwd@kb7pwd.ampr.org
 __) | | \________________________________________________________________
 Free long distance at http://www.bigredwire.com/me/RefTrack?id=USA063420