Star-forming dwarfs are studied to elucidate the physical underpinnings of their fundamental plane. Processes controlling dynamics are evaluated, connections between quiescent and bursting dwarfs are examined, and the viability of using structural properties of dwarfs to determine distances is assessed. Deep surface photometry in K super( s) is presented for 19 star-forming dwarfs. The data are amalgamated with previously published observations to create a sample of 66 galaxies suitable for exploring how global properties and kinematics are connected. It is confirmed that residuals in the Tully-Fisher relation are correlated with surface brightness, but that even after accommodating the surface brightness dependence through the dwarf fundamental plane, residuals in absolute magnitude are far larger than expected from observational errors. Rather, a more fundamental plane is identified which connects the potential to HI line width and surface brightness. Residuals correlate with the axis ratio in a way which can be accommodated by recognizing the galaxies to be oblate spheroids viewed at varying angles.