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Jellyfish are majestic, energy-efficient, and one of the oldest species that inhabit the oceans. It is perhaps the second item, their efficiency, that has captivated scientists for decades into investigating their locomotive behavior. Yet, no one has specifically explored the role that their tentacles and oral arms may have on their potential swimming performance. We perform comparative in silico experiments to study how tentacle/oral arm number, length, placement, and density affect forward swimming speeds, cost of transport, and fluid mixing. An open source implementation of the immersed boundary method was used (IB2d) to solve the fully coupled fluid–structure interaction problem of an idealized flexible jellyfish bell with poroelastic tentacles/oral arms in a viscous, incompressible fluid. Overall tentacles/oral arms inhibit forward swimming speeds, by appearing to suppress vortex formation. Nonlinear relationships between length and fluid scale (Reynolds Number) as well as tentacle/oral arm number, density, and placement are observed, illustrating that small changes in morphology could result in significant decreases in swimming speeds, in some cases by upwards of 80–90% between cases with or without tentacles/oral arms.