Granting COPY FROM access

[post header corrected, sorry]

I have an application that uses ODBC to access a PostGreSQL 8.0.3
database. To load in text files (comma separated, with column headers),
I use the SQL statement COPY FROM, which requires me to be a superuser.
I don't need full superuser access, so I would like to restrict the
permissions to only those necessary. The GRANT doc says that INSERT
privilege allows COPY FROM, so as a superuser I did something like
"GRANT INSERT ON my_database TO regular_user".

Unfortunately, when I login to my_database as regular_user, I don't
have permission to do COPY FROM. So, my question is: can COPY FROM
permission be granted to a non-superuser, or is there something else
that I missed?

-Jim Cser