We proposed here a sequential rather than a simultaneous consensus strategy, first using the FtsZ crystallographic small binding-cavity and then the wider grid-dependent docking program AutoDockVina (ADV). The search was first restricted to the binding cavity to best explore large chemical spaces by random generation of children molecular libraries (libraries on automatic demand) and automatic selection by fitting the limits of docking-scores, molecular weight and hydrophobicity (DataWarrior). After filtering the children libraries for toxicity, a consensus docking with AutoDockVina generated a final downsized list of new lead chemotypes. Because such strategy allows a first fitting to the selected docking-cavity for ligands controlling docking to cavity, sizes and hydrophobicity, the ligand efficiency (ligand binding per molecular weight or non-hydrogen compounds) may be maintained or even increased during evolution. The generated children libraries can then be ranked not only by docking-scores but also by ligand efficiency parameters. Additionally, to computationally increase the probabilities of bacterial cell wall penetration, some of the bacterial eNTRY rules for drugs were finally applied (i.e., primary amines and globularity).