  We present a method for calculating solutions and corresponding central
charges for backgrounds with AdS_3 and S^k factors in alpha'-exact fashion from
the full tree-level low energy effective action of heterotic string theory.
Three examples are explicitly presented: AdS_3 X S^3 X T^4, AdS_3 X S^2 X S^1 X
T^4 and AdS_3 X S^3 X S^3 X S^1. Crucial property which enabled our analysis is
vanishing of the Riemann tensor calculated from connection with "sigma-model
torsion". We show the following: (i) Chern-Simons terms are the only source of
alpha'-corrections not only in BPS, but also in non-BPS cases, suggesting a
possible extension of general method of Kraus and Larsen, (ii) our results are
in agreement with some conjectures on the form of the part of tree-level
Lagrangian not connected to mixed Cern-Simons term by supersymmetry (and
present in all supersymmetric string theories), (iii) new alpha'-exact result
for central charges in AdS_3 X S^3 X S^3 X S^1 geometry. As a tool we used our
generalization of Sen's entropy function formalism to AdS_p with p>2, and paid
special attention to proper definition of asymptotic charges.
