  We present kinematic analyses of the 12 galaxies in the "Survey of HI in
Extremely Low-mass Dwarfs" (SHIELD). We use multi-configuration interferometric
observations of the HI 21cm emission line from the Karl G. Jansky Very Large
Array (VLA) to produce image cubes at a variety of spatial and spectral
resolutions. Both two- and three-dimensional fitting techniques are employed in
an attempt to derive inclination-corrected rotation curves for each galaxy. In
most cases, the comparable magnitudes of velocity dispersion and projected
rotation result in degeneracies that prohibit unambiguous circular velocity
solutions. We thus make spatially resolved position-velocity cuts, corrected
for inclination using the stellar components, to estimate the circular rotation
velocities. We find circular velocities <30 km/s for the entire survey
population. Baryonic masses are calculated using single-dish HI fluxes from
Arecibo and stellar masses derived from HST and Spitzer imaging. Comparison is
made with total dynamical masses estimated from the position-velocity analysis.
The SHIELD galaxies are then placed on the baryonic Tully-Fisher relation.
There exists an empirical threshold rotational velocity <15 km/s, below which
current observations cannot differentiate coherent rotation from pressure
support. The SHIELD galaxies are representative of an important population of
galaxies whose properties cannot be described by current models of
rotationally-dominated galaxy dynamics.
