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All main-sequence stars are magnetic somewhere in their interiors. In most cases those magnetic fields are built by dynamo action, and ultimately sustained by convective motions within the star. This convection must be maintained against viscous and Ohmic dissipation, but little previous work has considered the role this dissipation might play in influencing the convection, the magnetic fields that are built within the interior, or (ultimately) the structure of the star. Here, we outline some results from a series of both local and global MHD simulations, and from basic theory, which provide some constraints on the overall level of dissipation and how this is intertwined with the strength and morphology of the magnetic fields. We also discuss claims that particularly strong magnetic fields may affect the structure and radii of low-mass stars; we argue that the extreme field strengths required in some of these models are ruled out by the complementary constraints of buoyancy and dissipation. Finally, we note some possible consequences of dissipation for the structure of low-mass stars.