Well - "BUMP".
I made a work around - it turned out that I could use java script in the html code.
I now have followning: Open the joomla page in a new window. and inserted this in the submit line:
<input onclick="javascript: setTimeout(window.close, 400);" type="submit" value="SEND" /> <input type="reset" value="CLEAR" />
It lets the page timeout after 400 milisec, then it closes. Hope it works in all browsers - only checked it in firefox so far.
It is now 100% what I wanted, but it does the job more or less. No waiting time for the users after posting and the form is posted - some secrecy is maintained due to the relatively fast closure of the window/popup.