Removing front license plate that has rivets...

[Sabre]

Okay I've got a front license plate on my car I want to remove.  In the pic below you see it's held on by three rivets.  I've never removed a front license plate with rivets before.  Anyways I looked up on the internet that you need to drill the rivets out.  The advice I read was that you take a 1/8 drill bit which is slightly larger than the "hole" in the middle of the rivet.  You drill into the center of the rivet until you go through.  After which the rivets should come off and the front license plate can be removed.  Well yesterday I had some time and took a drill with a 1/8 drill bit.  I drilled through all three rivets pictured below and nothing....  Nothing came off, nothing came loose at all.  The front license plate is still secured to the front bumper.  So my question is now what?  There is no way to see behind the bumper on my car (unless the front bumper is removed).  Do I drill again with a slightly larger drill bit?  Is there a special drill bit used to remove rivets like these, if so what is the name of it so I can order one.  Sorry if I sound like a complete noob/idiot.

FYI the pic below is BEFORE drilling the rivets.

[Aero426]

You are going to need to use progressively larger bits.  It will come off. 

[daveco]

Those are probably more like 3/16" or 1/4" dia. shank rivets. Just keep going up one size drill at a time or use a unibit.

[Sabre]

Thanks guys, finally got the rivets out.  Too bad I have three holes, I bought some of those bumper plugs.  In the future I'll take it to a body shop and get the front (holes filled in) and rear bumper repainted.