I found this Persian stitch used in Kerman embroidery on the website of Arts and Design.
If I have understood it correctly Kerman Stitch is often used in Pateh embroidery on woollen shawls. The stitches are worked so densely they fill every bit of the fabric underneath, and you would think it is a Long and Short Stitch.
It is easy, and I assume it would be a good filling stitch for Canvas Work, too.
Work Kerman Stitch like this: