  We show that a set of small box counting dimension can be covered by a
H\"older graph from all but a small set of directions, and give sharp bounds
for the dimension of the exceptional set, improving a result of B. Hunt and V.
Kaloshin. We observe that, as a consequence, H\"older graphs can have positive
doubling measure, answering a question of T. Ojala and T. Rajala. We also give
remarks on H\"older coverings in polar coordinates and, on the other hand,
prove that a Homogenous set of small box counting dimension can be covered by a
Lipschitz graph from all but a small set of directions.
