Best way to cover gray

I am naturally redish-auburn....so I try and stay in that same family to color my hair, which I do to cover the grays.  I was once told that the lighter I go, the better the gray coverage, but I find this not to be true as I find when I use my darker 'winter' color, the gray covers better.  I like to go a little lighter in the spring/summer, but it's like the grays don't cover at all....any suggestions as to perhaps brands, or colors, or techniques to use to cover gray hairs better?

Thanks to any and all who respond!