  We conduct a comparative analysis of the constants in the Nagaev-Bikelis and
Bikelis-Petrov inequalities which establish non-uniform estimates of the rate
of convergence in the central limit theorem for sums of independent random
variables possessing finite absolute moments of order $2+\delta$ with
$\delta\in[0,1]$. We provide lower bounds for the above constants and also for
the constants in the structural improvements of Nagaev-Bikelis' inequality. The
lower bounds in Nagaev-Bikelis' inequality and it's structural improvements are
given in dependence on $\delta$ and a structural parameter $s$ as well as
uniform with respect to both $\delta$ and $s$. Lower bounds for the constants
in Nagaev-Bikelis' with $\delta<1$ and Bikelis-Petrov's inequalities are
presented for the first time.
