There are more ways to maximize the fabric you have available for binding. One is Tartan's way. You can put that on upside up or upside down. If it is upside down, the "scrap" will be mostly showing and the "good" fabric will be a flange. So you would make the scrap side in fabric that you want to show.
More savers: Don't cut off your selvages. They will be mostly cut off as you make your seam on the diagonal. The tiny bit still on there is then in the seam allowance. I usually cut off the very ends that are very thick. Less than 1/8 of an inch.
Don't make 45º seams when joining strips. I lay my strip on the line on the mat with the end of the strip on a line and the strip edge on a line. Lay the another strip overlapping this just one inch. Use a ruler to cut across on the angle from the end of one strip to the end of the other one. The lines on the mat will show you where that is. Lift ends of strips right sites together and make the seam. The resulting slant is not 45º, but it's enough to keep bulk from the seam from piling up in one place.
I hope you can understand this. I do this even if there is plenty of fabric. I like to use leftovers in my scrap quilts.