  In this paper we introduce the confinement into the kernel of the BFKL
equation,assuming that the sizes of produced dipoles cannot be large. The goal
of this paper is to find how this assumption, which leads to a correct
exponential decrease of the amplitude at large impact parameters, affects the
main properties of the BFKL Pomeron. We solve the equations for total cross
section and $\ <| b^2 |\ >$ numerically and developed some methods of
analytical solutions. The main result is that the modified BFKL Pomeron has the
same intercept and $\alpha'_\pom = 0$ as the BFKL Pomeron.It gives us a hope
that the unknown confinement will change only slightly the equations of the
CGC/saturation approach
