Reduce bleed through for double sided document scan

I scanned some old documents which have print on each side. When scanned, there was significant bleed through from the reverse side in the image output. A couple example pieces of the image follow.

The print on the reverse side comes through pretty strong. The inside of the scanner cover is white, which will certainly reflect more light. I decided to put black construction paper on top of the document to see if it would help.

The scan with the black backing significantly reduces the bleed through of the text on the reverse side. The black backing does darken the scanned image, but it can be brightened up using an image editing tool.

The top two images show the scan results with the black backing. The next two images are the scans without the black backing. It is not perfect, but I'm happy with the result.

I hope this helps someone else :-)