This is more or less a reminder to self because I don't do this often enough to remember it :-)

My thought is that if I write a blog post about it and I won't forget anymore and I might be able to help someone with this (altough when you Google on it there are numerous useful articles about this topic).

So here it is:

How to change the connection of a clip to another clip in FCP X

You can change the point where a clip is connected by pressing command+option (cmd+alt) and clicking on the clip that has the connection and on the position where you want the new connection to be. See the video of a demonstration of this.