It is known that a set of k intergers with small doubling (small —A+A—) satisfying the condition —A+A—=2k-1+b,b in [0,k-3] is a part of arithmetic progression of k+b terms. It appeared that the structure of A may be described in a much more detailed way. The similar result may be obtained for difference A-A and for the sum A+B of two different sets A and B.