  We discuss the extension of the HKLL (Hamilton, Kabat, Lifschytz, and Lowe)
bulk reconstruction for non-interacting scalar fields corresponding to
conformal weights $\Delta$ smaller than the original condition $\Delta > d-1$.
We give explicit formulas for the cases $d-2<\Delta\leq d-1$ and $\Delta=d-s$
with integer $s$. In the latter case we show that smearing CFT fields over a
region of the boundary consisting of points light-like separated from the bulk
point is sufficient for bulk reconstruction, whereas in general smearing over
all light-like and space-like separated points is required.
