I'll try your settings - thank you :-)

Your talking about the message notifications that accumulate here in Galt's Gulch, right? Messages you see when you click the envelope icon (next to your name in the upper right-hand corner), right?

If so, unfortunately, there is currently no bulk delete feature for those. I'll pass your suggestion along though.

Personally, I just let them build up versus going to each comment notification and clicking delete.

I do not get any notices like that, TomB. Perhaps it will help to know what all my preferences look like:
Message Preferences
Yes Receive new comment notification emails
No Receive "Daily Digest" emails
Yes Receive new "Local Post" emails
No Auto-subscribe to "Local Post" comments
Yes Accept Private Messages from Gulch Producers
No Receive Private Message comment notifications

(Note: I do get email comment notices.)

I do appreciate your help, but I have already done that. Emails are turned off.
What I want to turn off is the notices of new messages (icon next to my name) when the message is that someone has posted on a thread that I posted. I can't find a way to mass delete when, for example today in response to one of my posts, 23 people replied, and I got 23 messages saying someone replied. That is all those messages say. So I have to click and confirm 23 times that I want to delete those. Getting those nonsense notices is what I want to stop.
I still go to the thread to read the replies.

Why are you here if you don't want to read comments?

It is a feature of the WSJ or NYT.

If you don't want to have comments you should not be on this board.

Click on the down arrow next to your handle/name in upper right of the screen.
In the pull down menu click on Edit Settings.
In Message Preferences
Un-check Receive new comment notification emails

I think that should work ;^)