In reply to BigBrother:
> Is my method no longer used because it is now considered dangerous for some reason?
No, it's just gone out of fashion a bit. IMO more because 3 decades of advertising by equipment manufacturers have succeeded in convincing climbers to carry more carabiners than any other reason.
However, despite your contention we need more discussion of knots we haven't really had any proper discussion of the knot itself yet.
It is a Figure-of-Eight Hitch tied on the bight. As knots go, the Figure-of-Eight Hitch it is actually pretty poor in terms of security as any research would quickly determine. However it does have other useful attributes.
From
http://www.scoutingresources.org.uk/downloads/knots_fig8hitch.pdf
Figure-of-Eight Hitch This hitch can be tied very quickly and is easy to untie. However it is not very secure.
The good news is that tied on the bight it is more secure than tied normally, but it is certainly be prudent to tie it with a generous tail. Fortunately, a long tail aids tying it quickly so this generally happens fairly naturally. Having given the knot very serious consideration over a number of years, I am content it is secure enough when used as you described, but it is worth being aware of its potential disadvantage.
For the excessively paranoid there are certainly more secure options.
IMO the best option is probably tying a buntline hitch on the bight. This is extremely secure and suits climbers to the extent that after starting in the same manner as the Figure-of-Eight Hitch you effectively tie a clove hitch (with which most climbers are already familiar) back around the standing rope using your bight. See
http://www.scoutingresources.org.uk/downloads/knots_buntlinehitch.pdf
Another potentially simpler option, as a poster has already mentioned is to tie Two Half Hitchs on the bight.
HTH