Inspiration for this tutorial comes from Richard Hayler. Without it, I would have had no clue what to do. Thank you Richard!
http://richardhayler.blogspot.ca/2015/10/squeezing-raspbian-jessie-on-to-4gb-sd.html
You will need to start with three cards:
- the target 4Gig,
- the origin 8Gig card
- and an intermediate 16Gig card.