You can adjust the mechanism that connects the handle to the latch. You have to pull the door panel. There is a threaded rod from the latch mechanism that connects to the handle via a white nylon 'grabber' part. The 'grabber' can be undone with a flat screwdriver, prying it apart. The threaded rod can then be moved up a little, the grabber reconnected, lubricate everything in sight, and you should be good.
Continued attempts to pull that handle up enough to open the door will eventually break the handle, I've sold 1/2 dozen or so on ebay because of that.