Pseudomonas aeruginosa has three type VI secretion systems (T6SSs), H1-, H2-, and H3-T6SS, each belonging to a distinct group. The two T6SS components, TssB/VipA and TssC/VipB, assemble to form tubules that conserve structural/functional homology with tail sheaths of contractile bacteriophages and pyocins. Here, we used cryoelectron microscopy to solve the structure of the H1-T6SS P. aeruginosa TssB1C1 sheath at 3.3 Å resolution. Our structure allowed us to resolve some features of the T6SS sheath that were not resolved in the Vibrio cholerae VipAB and Francisella tularensis IglAB structures. Comparison with sheath structures from other contractile machines, including T4 phage and R-type pyocins, provides a better understanding of how these systems have conserved similar functions/mechanisms despite evolution. We used the P. aeruginosa R2 pyocin as a structural template to build an atomic model of the TssB1C1 sheath in its extended conformation, allowing us to propose a coiled-spring-like mechanism for T6SS sheath contraction.