The molding I intend to use came with one of those metal trim strips. I don't want to use the strip, just glue straight to the floor. The problem is that without the strip, the molding is just a bit too short. What can I use to shim up the molding a tiny bit? Will a thick bead of adhesive make up the difference?

How much space are we talking about here??

Also, what moulding piece is it? Pictures would be helpful too.

I fill the gully) or almost. Then place my molding and let it ooze out. Come back the next day or later after it has set up, and take my hawk bill knife and remove the oozed blobs, and use mineral spirits to clean any residue of glue.

The space is probably 1/8th or even a tad bit less. I did the glob test Floorguy referred to (before I read the responses) and it seems that it will work. The piece is a T-molding ripped in half length-wise to form a sort of square nose. And I am placing at my front door under the sidelight casings. Should work out. Thanks for the advice.