What is the equivalent for "service servicename start" that Fedora/RHEL/CentOS uses for Debian/Ubuntu?

What is the equivalent for "service servicename start" that Fedora/RHEL/CentOS uses for Debian/Ubuntu?
I've just read on some question here on serverfoault that using /etc/init.d/service is obsolete, so what's the correct way on Debian?

From serverfault daniels

• I don't know about the "correct" way, but I always use invoke-rc.d, so e.g. to restart MySQL:

  sudo invoke-rc.d mysql restart
  

  From Jörg W Mittag

• Yep, that's what I use too. /usr/sbin/invoke-rc.d is the way to go.

  From Red Five

• You can always just invoke the startup scripts directly (e.g., /etc/init.d/foo restart). This works on RedHat variants as well, although the path is slightly different there (/etc/rc.d/init.d, although I believe /etc/init.d is a symlink to it as well).

  Dave Drager : I use /etc/init.d foo stop|start|restart as well.

  Ophidian : Cribbing from a comment on another question (http://serverfault.com/questions/30701/how-to-enable-sshd-on-fedora-11), directly calling /etc/init.d/servicename is discouraged on Fedora/Red Hat systems. You also don't necessarily get the same environment provided to the scripts as you would using the /sbin/service script (e.g. on SELinux Gentoo you need to use `run_init` instead of /etc/init.d to get things to start in the correct security context.
  From ktower

• Whatever about on Redhat systems, /etc/init.d/service is still the norm on debian derivatives.

  From Cian

• all most every distro has /etc/init.d/service ****** {start|restart|reload|stop}

  From Rajat

• I suggest that you read about Upstart:

  http://upstart.ubuntu.com/

  http://www.linux.com/archive/feature/125977

  http://www.netsplit.com/category/tech/upstart/

  It is used on:

  • Ubuntu 6.10 and later
  • Fedora 9 and later
  • Debian (as an option)
  • Nokia's Maemo platform
  • Palm's WebOS
  From Dennis Williamson

• The same service <servicename> start works for me in Ubuntu 9.04. It is in the sysvinit-utils package.

  From Juliano

• Using /etc/init.d/foo on RedHat can cause problem if selinux is activated because the script should not set up the context correctly. The service command always works on selinux enabled RHEL.

  From Saabi