We determine and compare, at the single molecule level and under identical environmental conditions, the electrical conductance of four conjugated phenylene oligomers comprising terminal sulfur anchor groups with simple structural and conjugation variations. The comparison shows that the conductance of oligo(phenylene vinylene) (OPV) is slightly higher than that of oligo(phenylene ethynylene) (OPE). We find that solubilizing side groups do neither prevent the molecules from being anchored within a break junction nor noticeably influence the conductance value.