Styles get mixed up in Word when pasting from another document

There are a lot of different explanations showing how to keep source or destination document formatting when pasting text from one document to another. One thing however seems to be missing in all these descriptions and that is when the destination document is completely new. In this case, the source style formatting always seems to override the destination. Like shown below where a .doc text fragemnt with certain styles for headers, is pasted into a .docx default header style document. As can be seen, the Heading 1 formatting has taken the form of the pasted document, whereas Heading 2 is kept in its original form from the .docx document.

The trick is to first enter some text containing all kind of styles that shall be kept, i.e. enter some text with Heading 1, Heading 2 etc. and then paste text from other documents. In this case the buttons on the clipboard dialog can be used to select the wanted formatting.