The Brick stitch is one of my favourite fill stitches, especially if you need to fill in relatively large areas in your embroidery. At least I assume it's called the Brick Stitch because I only found a hand full of references to this stitch in my small Embroidery Library and online. And it's such a useful stitch to know! (If anyone has more info please let me know) Apparently there are two ways of performing this stitch.
What I usually do is much like building a wall with Lego blocks. I stitch rows of Back stitches of the same length (ahem, ideally the same length that is) starting from left to right ( I'm left handed). I start the second row with a half length Back stitch and continue with normal length Back stitches until I reach the end of the row finishing again with a half length stitch. This is a rather quick filling method which can look a tiny bit bulky because of the 'roundness' of the Back stitch.
In Mary Thomas' Dictionary of Stitches I found another method that, to me, is awfully similar to the Long Short Stitch. I have used different colours to show how it's build up. I started with the darker shade of blue stitching a row alternating a long and a shorter stitch. After that I stitched a row, in a lighter shade of blue, filling in the gaps between the longer blue stitches, after that a row in white floss in the same way etc etc. Not as quick as method number one but certainly more neat and less bulky. It's also, like the Long Short Stitch, perfect for shading.
Hope you have enjoyed my little exploration of the Brick Stitch.