LetMe0 be the maximal operator over segments of length 1 with directions belonging to a Cantor set. It has been conjectured that this operator is bounded onL2. We consider a sequence of operators over finite sets of directions converging toMe0. We improve the previous estimate for the (L2,L2)-norm of these particular operators. We also prove thatMe0 is bounded from some subsets ofL2 toL2. These subsets are composed of positive functions whose Fourier transforms have a very weak decay or are supported in a vertical strip.