Here's a regraining tip I learned today!
I have typically used varying grits of sandpaper in the past to regrain. A friend suggested I try scotch-brite pads. So, I tried them, worked OK but not as good as the sandpaper. I found out that there are different types of scotch-brite style pads. The one that is recommended is red or maroon in color, and made by 3M and sold for metal refinishing.
I got a couple red 3m sanding 'pads' (not like the sponges), and they worked great! Much better than the green ones!