We present an analysis of newly discovered velocity-coherent structures in the L1688 region of Ophiuchus and the B18 region of Taurus.   The structures are identified in a search of ammonia spectral cubes from the Green Bank Ammonia Survey (GAS; \citealp{Friesen2017}) alongside Herschel maps of thermal dust emission, looking for regions of high density and near-constant, almost-thermal, velocity dispersion.  Eighteen coherent structures are revealed, twelve in L1688 and six in B18, each of which shows  a sharp "transition to coherence" in velocity dispersion around its periphery.  We call these structures "droplets," and  we show that they are smaller cousins of the coherent cores previously identified by \citet{Goodman1998}, \citet{Caselli2002}, and \citet{Pineda2010}.  The droplets have a typical size (radius) of ~0.04 pc and a typical mass of ~0.3 M_⊙.  Unlike previously known coherent cores, droplets are gravitationally unbound according to a virial analysis.  The droplets are, instead,  likely confined by pressure due to thermal and non-thermal (turbulent) motions of ambient gas.  Droplets show shallow radial density profiles, and they sometimes sit at local line-of-sight velocity extremes.  We investigate several potential formation mechanisms for droplets, and speculate on the role that droplets, and  coherent structures more generally, may play in the process of star formation.