Miagirl Ishtari

Can anyone make their avi invisible to their connections while in SL? I know that in "My Second Life" homepage, you can click on an Avi and in the "Permission" options, you can uncheck "See my online Status", but that will only make them invisible on the dashboard's people list. If you go to their profile and they're in SL, they will appear online. Is there any other way that an avi can stay invisible even if one goes to his/her profile? Thanks.