We are concerned with the Cauchy problem for the KdV equation for nonsmooth locally integrable initial profiles qs which are, in a certain sense, essentially bounded from below and q(x)=O(e^{-cx^{{epsilon}}}),xrightarrow+infty, with some positive c and {epsilon}. Using the inverse scattering transform, we show that the KdV flow turns such initial data into a function which is (1) meromorphic (in the space variable) on the whole complex plane if {epsilon}>1/2, (2) meromorphic on a strip around the real line if {epsilon}=1/2, and (3) Gevrey regular if {epsilon}<1/2. Note that qs need not have any decay or pattern of behavior at -infty.
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