Cross-flow or vertical-axis turbines are flow energy conversion devices in which lift forces cause blades to rotate around an axis perpendicular to the flow. In marine currents, rivers, and some wind energy applications, cross-flow turbines are a promising alternative to more conventional axial-flow turbines. The performance implications of the choice of structure used to mount turbine blades to the central shaft are examined experimentally in a recirculating water flume. Turbine performance is found to be strongly dependent on the choice of the mounting structure. Power loss due to rotational drag on these structures is estimated experimentally by rotating the mounting structure without blades. Through a perturbation-theory approach, interactions between turbine blades and mounting structures are examined. Analytical models for the power loss due to mounting structure drag are introduced and shown to be consistent with experiments. To provide guidance for cross-flow turbine design, the models are re-formulated in terms of non-dimensional turbine geometric and operational parameters. Mounting blades solely at their mid-span is shown to decrease performance through multiple fluid effects. Using foil cross-section struts located at the turbine blade tips is found to result in the highest turbine performance.