I have now found, that you are right rknichols; the LF's are not in the text file.
It seems that the LF's are introduced by the display program, because, it turns out, that "cat" displays the file OK (i.e. with CR and no LF), while "gedit" gives too many lines (i.e. with both CR and LF).
LibreOffice Writer on the other hand displays the file in a third way, as one long line, i.e. without both CR and LF.
My problem is now if there is a way to make the text file independent of the display program.