Orthogonal arrays (OAs) of strength 2 permit independent estimation of main effects. An orthogonally blocked OA could be considered as an OA with one additional factor. Such an OA is in fact a two-stratum design. The main effects of the treatment factors are estimated in the bottom stratum. The upper stratum may contain interaction components for these factors. The blocking factor supposedly has no interactions with treatment factors. I propose to search for suitable blocking arrangements by studying projections of arrays into those with one factor less. I illustrate with a complete catalogue of blocked pure or mixed 18-run arrays.