Tiling deficient staircase regions with L-trominoes

We consider the problem of tiling staircase regions with L-trominoes. In particular, in case such a tiling is not possible, we investigate if the situation changes if we remove one 1 × 1 square from the staircase region and if the position of the removed square plays a role. We give a complete solution to this question. Moreover, we use our results to infer the tileability of some regions that are composed of several staircase regions.