There are three options to solve the puzzle you are giving:
a) according to your description, especially the crossing to make sure only a certain person can cash in, leads me to believe that you are talking about a "Order-Scheck". In order to get one you need to have an account with the bank so, it is not common to pay for it. In my experience it is only handed out to companies and not to private persons but I might be wrong.

what the other side, the recipient of the cheque might be looking for, though, is a cheque that can't bounce (which the order cheque can). This would best be acchieved with a "LZB-Scheck" which only the public Landeszentralbank can issue (though you should be able to get one through your bank but expect several days if not weeks before you have it). Here you pay in the full amount plus fees and the LZB delcares that the cheque is always good for this money.
c) the third option could be a "Sichtwechsel" or demand draft/bill payable on sight. This again requires good standing with your bank and since this is counted as an AVAL-Kredit it is more common nowadays for companies but should be available to private persons. But a demand draft could legally still bounce (even though penalties are rather harsh and thus the risk rather low), therefore I assume your recipient would rather have a LZB-SCheck.
Hope this helps and explains more than it confuses...
Cheerio