Paste from clipboard and center

When I paste from the clipboard onto a smaller document, the image puts both top left corners together.
How can I center the pasted image so when I scale down the pasted image it stays exactly in the center?

The drag and drop holding shift centers the image like I would like, but Shift and paste still lines up both top left corners.

I used copy merged so the drag and drop is not always useable.

Am I explaining this clearly?

Yes.
I can't think of a way to do it at paste time, but you can do it in a few clicks: After pasting, do a select all, switch to the move tool to click on the 2 align to center buttons

Different, but just as effective is Ctrl+'A' to select all, Ctrl+'X' to cut, then Ctrl+'V' to paste, which will center your object.

Maddy, dougleax asks for clipboard pastes, one can't do that with your method, unless I missed something? I can't replicate it... (I tried with printscreen?)