For theming reasons I'd like to add a specific class at the "block" level to some of the blocks I'm generating with a custom module. I know there is a module block class, but I would rather like to do it directly in code (there is no need to change is afterwards).
I also know of hook_block_view_alter, but that does not seem to allow adding or editing classes.
Is it possible to add a class with to a block from within my module code? I'm using Drupal 7.