The dog has started to act uncomfortable in coming up the stairs from the back yard to the deck at night. Linda suggests it is because of the contrast in lighting between the deck (with its two new bright LED light fixtures) and the yard.
So we purchased two LED lights to shine on the deck stairs. Since we have no power to this location, these are solar powered LED lights. The stairs face South and have no shade (at least until the Pecan tree gets much bigger), so this should work well.
We bought two Solar Step Lights from Amazon (JackyLED brand, $12.99).
and installed one on each side of the stairs.
The biggest problem was the installation. There are two screws which must be exactly the right distance apart (7.6 cm according to the instructions), but we traced the back of the light onto a piece of paper and then drilled holes using that as a template. However, despite drilling holes for the screws, the screws were made of such soft metal that they broken when screwing into the deck wood. Remember the deck is ipe (iron wood), and very hard. Luckily I had alternative screws that worked better.
The lights themselves seem to work really well -- very bright and last most of the night.