Searching way to **not** send mail after user registration I want user from a certain domain to be able to register without approval, while others need te be approved by a user manager.

I defined a rule that after a new user registers, through text comparison on the user's mail address, checking if it is from the "safe" domain, unblocks the user. This works very well, but Drupal will send both the mails: 
 - welcome, pending approval and
 - your account has been approved.

Is there a way to achieve that the welcome, pending approval mail is not sent?

Is there a way using rules where you can rule out Drupal actions, like saying: "When this happens, do not take that action?"
Mailcontrol worked like a charm.
If you are looking for the configuration it is right with the Drupal user configuration. 

it provides the necessary UI additions for D7 (and D8) to enable site admins to enable/disable any standard Drupal mail