In the process of rebuilding my site, I decided to build from scratch, rather than attempting to upgrade my installation. With my old installation, I had tried out multiple modules, changed themes multiple times, and played around with the database when I didn't fully know what I was doing, leaving me with a system that worked, but at times was buggy. For this reason, I thought it better to build fresh and import.
As such, I needed to import the comments from my Drupal 6 installation to my new Drupal 7 installation. This is easier said than done - comments have received a major restructuring, and use different database tables in Drupal 6 than they did in Drupal 7, and the column names the comment system uses has also changed.