How do I disable the discussion notification emails to us when a comment is “approved” and when an adiministrator replies?

We have all comment notifications being emailed into our ticketing system (Freshdesk) and it’s getting a bit muddy because of the redundant notifications.

What is currently happening:

1. A site visitor makes a comment that is held for approval and an email is sent to us:
   "A new comment on the post "X" is waiting for your approval" = GOOD
2. When the comment is approved by an admin, another email is sent to us: "New comment on your post "X"" = BAD
3. When an administrator replies to a comment, another email is sent to us: "New comment on your post "X"" = BAD

In our WordPress Discussion Settings, under the "Email me whenever" subsection, we have both "anyone posts a comment" and "a comment is held for moderation" checked. Under the "Before a comment appears" subsection, we have "comment must be manually approved" checked.

What settings do I need to change to turn off the emails in 2 and 3 above?