Super-simple designs can be used to provide samples with maximum intersection as small as possible in statistical planning of experiments and can be also applied to cryptography and codes. In this paper, super-simple pairwise balanced designs with block sizes 3 and 4 are investigated and it is proved that the necessary conditions for the existence of a super-simple (nu,{3, 4}, lambda)-PBD for 2 <= lambda <= 6 are sufficient with three possible exceptions. (C) 2016 Elsevier B.V. All rights reserved.