  We investigate the strong field lensing observables for the Damour-Solodukhin
wormhole and examine how small the values of the deviation parameter $\lambda $
need be for reproducing the observables for the Schwarzschild black hole. While
the extremely tiny values of $\lambda$ indicated by the matter accretion or
Hawking evaporation are not disputed, it turns out that $\lambda $ could
actually assume values considerably higher than those tiny values and still
reproduce black hole lensing signatures. The lensing observations thus provide
a surprising counterexample to the intuitive expectation that all experiments
ought to lead to the mimicking of black holes for the same range of values of
$\lambda$.
