  We present structural improvements of Esseen's (1969) and Rozovskii's (1974)
estimates for the rate of convergence in the Lindeberg theorem and also compute
the appearing absolute constants. We introduce the asymptotically exact
constants in the constructed inequalities and obtain upper bounds for them. We
analyze the values of Esseen's, Rozovskii's, and Lyapunov's fractions, compare
them pairwise and provide some extremal distributions. As an auxiliary
statement, we prove a sharp inequality for the quadratic tails of an arbitrary
distribution (with finite second order moment) and its convolutional
symmetrization.

Probability