The viscosities of dimethyl ether (DME, C2H6O) and of the fluorinated propene isomers 2,3,3,3-tetrafluoroprop-1-ene (R1234yf, C3H2F4) and trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) were measured in a combined temperature range from 242 K to 350 K at saturated liquid conditions. The instrument was a sealed gravitational capillary viscometer developed at NIST for volatile liquids. Calibration and adjustment of the instrument constant were conducted with n-pentane. The repeatability of the measurements was found to be approximately 1.5 %, leading to a temperature-dependent estimated combined standard uncertainty of the experimental data between 5.7 % at 242 K for dimethyl ether and 2.6 % at 340 K for R1234yf. The measurements were supplemented by ab initio calculations of the molecular size, shape, and charge distributions of the measured compounds. The viscosity results for dimethyl ether were compared with literature data. One other data set measured with a sealed capillary viscometer and exceeding the present results by up to 7 % could be reconciled by applying the vapor buoyancy correction. Then, all data agreed within the estimated uncertainty of the present results. Viscosities for the fluorinated propene isomers deviate up to 4 % from values predicted with the NIST extended corresponding-states model. The viscosities of the two isomers do not scale with their dipole moments. While the measured viscosity of R1234ze(E) with the lower dipole moment is close to that of R134a, the refrigerant to be replaced, that of R1234yf with the higher dipole moment is up to 25 % lower. The viscosity of dimethyl ether is compared with those of water and methanol.