How to successfully punch shapes from thin tissue... without going nuts

I found a a beautiful paper napkin at the dollar store that I absolutely love, and I have collaged it onto just about every empty box I can find!  I even put it on one of those manikin heads you can find for wigs.

I decided I wanted to top one of the containers with a flower made from one of my favorite punches. This is very thin tissue indeed, particularly after having removed the inner white lining from the napkin.

I slid it into the punch, and this is what I got:

 Not only did it not punch properly, I had a dickens of a time getting it out of the punch.   So disappointed I was!

I refused to give up, and to make this flower to position it where I want I was going to need more than one of these shapes.  Then I thought, why not just "fool" the punch, and lay the tissue on top of a piece of cardstock?  Not adhered to it, because I want only the tissue for this particular project.  And it worked! Here was the result.. and it gave me, of course, extra flower shapes from the cardstock for a future use.

Simple solution, right?

I love my EK punches, but they are getting a bit cranky.  I had to use some WD40 on them this week because the springs were not too springy anymore.

SO happy at having found this solution!

Happy long weekend.