In this paper we investigate the effect of introducing transverse mome
ntum cutoffs on the BFKL equation. We present solutions in moment spac
e for various models of the BFKL kernel for different combinations of
these cutoffs. We improve on previous calculations by using the full B
FKL kernel (rather than simplified analytic approximations). The signi
ficance of the next-to-leading or ''higher twist'' terms in the kernel
are assessed. We find that, while these terms are negligible in the a
bsence of cutoffs, introducing an infrared (IR) cutoff markedly enhanc
es their significance.