Aims: 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. Methods: Deep surface photometry in Ks 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. Results: It is confirmed that residuals in the Tully-Fisher relation are correlated with surface brightness, but that even after accomodating the surface brightness dependence through the dwarf fundamental plane, residuals in absolute magnitude are far larger than expected from observational errors. Rather, a morefundamental 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. Correction of surface brightnesses to face-on leads to a correlation among the potential, line width, and surface brightness for which residuals are entirely attributable to observational uncertainties. The mean mass-to-light ratio of the diffuse component of the galaxies is constrained to be 0.88 ± 0.20 in Ks. Blue compact dwarfs lie in the same plane as dwarf irregulars. The dependence of the potential on line width is less strong than expected for virialized systems, but this may be because surface brightness is acting as a proxy for variations in the mass-to-light ratio from galaxy to galaxy. Altogether, the observations suggest that gas motions are predominantly disordered and isotropic, that they are a consequence of gravity, not turbulence, and that the mass and scale of dark matter haloes scale with the amount and distribution of luminous matter. The tight relationship between the potential and observables offers the promise of determining distances to unresolved star-forming dwarfs to an accuracy comparable to that provided by the Tully-Fisher relation for spirals. Based on observations acquired from CFHT, CTIO, ESO, OAN-SPM, and SAAO.