Molecular dynamics computer simulations were conducted on atomic clusters using constant energy and the Lennard-Jones 6-12 pair-wise potential, with emphasis on the liquid state. Large liquid clusters exist only at relatively high temperatures and have a large number of desorbing atoms, making the central cluster hard to identify and study. Multiple approaches to atom plucking were taken with a focus initially on potential energy plucking. Since most desorbed atoms have essentially zero potential energy, a potential energy cutoff is effective in plucking most desorbed atoms. However, larger clusters contained dimers and trimers which passed the initial potential energy plucking criterion; the existence of dimers was verified by visual analysis and neighbor statistics. An attempt was made to determine if a high but non-zero potential energy plucking criterion would ensure the plucking of all desorbed atoms and dimers without plucking atoms from the central cluster. A neighbor criterion plucking routine was also developed, to pluck dimers and trimers that passed potential energy criterion. Well plucked clusters were used to create two-dimensional histograms of potential energy (and other measures) versus radial distance for the core liquid cluster; this technique may eventually reveal new information about the structure of a cluster in the liquid state.