  We perform a detailed analysis of the different forms of the kinematical
constraint imposed on the low $x$ evolution that appear in the literature. We
find that all of them generate the same leading anti-collinear poles in Mellin
space which agree with BFKL up to NLL order and up to NNLL in $N=4$ sYM. The
coefficients of subleading poles vanish up to NNLL order for all constraints
and we prove that this property should be satisfied to all orders. We then
demonstrate that the kinematical constraints differ at further subleading
orders of poles. We quantify the differences between the different forms of the
constraints by performing numerical analysis both in Mellin space and in
momentum space. It can be shown that in all three cases BFKL equation can be
recast into the differential form, with the argument of the longitudinal
variable shifted by the combination of the transverse coordinates.
