We have this 1939 built house and we've taken all the doors off and sc****d and re-painted them and are re-hanging them with new hinges and installing new doorknobs.

One of the doors has this teeny tiny little doorknob that I must replace. It appears to be about 2 1/4" diameter, but the backset is the weirdest thing I've ever seen - it is SO close to the edge of the door. The backset is about 1 3/4" (measurement from the edge of the door to the center of the hole.)

I'm having trouble finding a replacement knob that comes with that short of a backset. And because it is so close, I can't just bore a new hole without still having a gap there.

Can I fill that gap with a block and wood putty and then just re-drill? (We're going to paint these doors, anyways.)

Does anyone know a resource for knobs that come with smaller backsets?

Thanks for your input,