I have ripped out some old carpet and am preparing to install a new solid hardwood floor myself. In several places, the floor transitions to an existing tile floor. The hardwood floor guys told me the best transition between the two is a T molding. You simply leave a gap between the two floors, and then place down the T molding between the two floors, so it sits on both surfaces. Sounds simple enough.

However, the height difference of the two floors is considerable, and the T molding does not sit flush. What are my options? Here is a diagram showing the dimensions. 

![floor transition diagram](https://i.stack.imgur.com/nzHZH.jpg)

NOTE: Using the T molding is not a requirement, I could go some other route if there is a better option.