join on a like

A friend suggested that I use the Like predicate as part of my join 
condition and I was wondering if that was wise.

For example, I have a column that describes the level of an event.
There is A,B,C and then they can have children, such as AA,AB,BA,BB and 
they can all have children as well.

So if I wanted to see all the children with their parents at every level 
it would be:
select a.* from tbl1 a join tbl1 b on a.level like b.level || '%'

That would give me on one side A and on the other side A,AA,AB,AAAB,...
as well as AA and on the other side all of its children.

I'm just nervous about using a Like in a join.