Inherent saddles of the potential energy surface, U, of a liquid are defined as configurations which correspond to the absolute minima of the pseudopotential surface, W=\delU\(2). Given finite numerical precision, multidimensional minimization procedures will sample both absolute and low-lying minima which are referred to collectively as quasisaddles. The sensitivity of statistical properties of these quasisaddles to the convergence criteria of the minimization procedure is investigated using, as a test system, a simple liquid bound by a quadratically shifted Lennard-Jones pair potential. The variation in statistical properties of quasisaddles is studied over a range of error tolerances spanning five orders of magnitude. Based on our results, it is clear that there are no qualitative changes in statistical properties of saddles over this range of error tolerances and even the quantitative changes are small. The results also show that it is not possible to set up an unambiguous numerical criterion to classify the quasisaddles into true saddles which contain no zero curvature, nontranslational normal modes, and inflexion points which have one or more zero-curvature normal mode directions. (C) 2003 American Institute of Physics.