We suggest that for singular rotationally invariant closed string back
grounds which need sources for their support at the origin (in particu
lar, for special plane waves and fundamental strings) certain 'trivial
' alpha'-corrections (which are usually ignored since in the absence o
f sources they can be eliminated by a field redefinition) may play an
important role leading to the absence of singularities in the exact so
lutions. These corrections effectively regularize the source delta-fun
ction at the scale of root alpha'. We demonstrate that similar smearin
g of the singularity of the leading-order point-charge solution indeed
takes place in the open string theory.