I recently figured out that you can specify the columns that you want to select from an eager loaded relationship in Eloquent. I thought others might find this useful as I couldn't find much about this online!
// Example: Post model belongs to an Author. We only want the name of the author.
$posts = Post::with(array('author' => function($query)
{
// Notice that you add either the primary key or the
// foreign key to the field list, or else Laravel
// won't be able to link the models together!
$query->addSelect(array('id', 'name'));
}))->get();
// To further explain the note I place within the closure, let's do it the other way around as well.
// Example: We only want the title of the posts.
$authors = Author::with(array('posts' => function($query)
{
// Notice the addition of the author_id field!
$query->addSelect(array('title', 'author_id'));
}))->get();