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Measuring locomotion tactics available to ancient sea animals can link functional morphology with evolution and ecology over geologic timescales. Externally-shelled cephalopods are particularly important for their central roles in marine trophic exchanges, but most fossil taxa lack sufficient modern analogues for comparison. In particular, phylogenetically diverse cephalopods produced orthoconic conchs (straight shells) repeatedly through time. Persistent re-evolution of this morphotype suggests that it possesses adaptive value. Practical lateral propulsion is ruled out as an adaptive driver among orthoconic cephalopods due to the stable, vertical orientations of taxa lacking sufficient counterweights. However, this constraint grants the possibility of rapid (or at least efficient) vertical propulsion. We experiment with this form of movement using 3D-printed models of Baculites compressus, weighted to mimic hydrostatic properties inferred by virtual models. Furthermore, model buoyancy was manipulated to impart simulated thrust within four independent scenarios (Nautilus-like cruising thrust; a similar thrust scaled by the mantle cavity of Sepia; sustained peak Nautilus-like thrust; and passive, slightly negative buoyancy). Each model was monitored underwater with two submerged cameras as they rose/fell over ~2 m, and their kinematics were computed with 3D motion tracking. Our results demonstrate that orthocones require very low input thrust for high output in movement and velocity. With Nautilus-like peak thrust, the model reaches velocities of 1.2 m/s (2.1 body lengths per second) within one second starting from a static initial condition. While cephalopods with orthoconic conchs likely assumed a variety of life habits, these experiments illuminate some first-order constraints. Low hydrodynamic drag inferred by vertical displacement suggests that vertical migration would incur very low metabolic cost. While these cephalopods likely assumed low energy lifestyles day-to-day, they may have had a fighting chance to escape from larger, faster predators by performing quick, upward dodges. The current experiments suggest that orthocones sacrifice horizontal mobility and maneuverability in exchange for highly streamlined, vertically-stable, upwardly-motile conchs.