Loose Door Knob

Our front door knob is loose. And it's really annoying, because both Eric and I have looked up "how to fix a loose door knob" online, and every reference is to a completely different type of knob. The one we have doesn't have a lock, and it has a latch that you press down on the outside and an ordinary-looking knob inside. But the knob is attached to the latch-side by sliding onto the screw heads that hold the latch-side in place! And the knob itself won't come off the mechanism, there's no "spring" to release it.

So I managed to take the knob off, and we both examined the door, and then I figured out how to put it back on... but I didn't get the screws in far enough, so it's still loose... however, at least it's on the door now instead of sitting on the table next to the door. I wish I could figure out an easy way to take it off so I could try again, but now it won't come off. *sigh* I could be a successful do-it-myselfer if I had any clue what I was actually doing.