  We discuss the use of the Gilbert algorithm to tailor entanglement witnesses
for unextendibleproduct basis bound entangled states (UPB BE states). The
method relies on the fact that an optimalentanglement witness is given by a
plane perpendicular to a line between the reference state, entanglementof which
is to be witnessed, and its closest separable state (CSS). The Gilbert
algorithm finds anapproximation of CSS. In this article, we investigate if this
approximation can be good enough toyield a valid entanglement witness. We
compare witnesses found with Gilbert algorithm and those givenby
Bandyopadhyay-Ghosh-Roychowdhury (BGR) construction. This comparison allows us
to learnabout the amount of entanglement and we find a relationship between it
and a feature of the constructionof UPB BE states, namely the size of their
central tile. We show that in most studied cases, witnessesfound with the
Gilbert algorithm in this work are more optimal than ones obtained by
Bandyopadhyay,Ghosh, and Roychowdhury. This result implies the increased
tolerance to experimental imperfections ina realization of the state.
