How to "upgrade" a dpkg with a .deb

[Matt England <mengland@mengland.net>]

How can one upgrade an installed dpkg with a .deb file, much the same way 
one can run:

   rpm -Uhv <new-version-of-package.rpm>

using rpm?  I was hoping for a

   dpkg -u <new-version-of-package.deb>

command, but I don't see this or anything like it.  I can't find anything 
in apt-get's man page, either.

Any suggestions, tips?

-Matt