Can't change title separator on homepage?

Hey.

I’ve got a bit of an issue with using the blog name and title separator. Here is my code as from the theme I’m using which I have edited to implement a ‘|’.

<title><?php

	if ( is_search() ) { echo "Search for $s"; }

	if ( is_404() ) { echo "404: Page Not Found"; }

	wp_title('|');

	if ( is_archive() ) { echo " archive "; }

	if ( !is_home() ) { echo " at "; }

	bloginfo('name');

?></title>

This works on all pages except the homepage. My homepage simply displays:

blogname – tagline

There is no | in sight. Forgive my novice PHP head. I assume the fix is very simple. Can anyone help?