The angular distributions of K- and of (L+M)-conversion electrons from oriented Ce137m nuclei were observed. Precise simultaneous intensity measurements of conversion electrons and γ rays from the same sample provided an accurate, direct determination of the particle parameters b2 associated with the 255-keV isomeric transition in Ce137. The K-electron result, b2=1.061 (18), is in excellent agreement with a theoretical prediction based on a "point nucleus" model. Techniques and parameters in this experiment, the first of its kind, are discussed. A more careful determination of the temperature dependence of anisotropy of the 255-keV γ ray yielded the value A=0.0147 (7) cm-1 for the hyperfine structure constant of Ce137m in neodymium ethylsulfate. This is slightly higher than the older value of 0.0129 (12) cm-1 found in this laboratory and is to be preferred on the basis of internal evidence. Using Bleaney's value of〈r-3〉4f=4.44 au, the derived magnetic moment is changed from 0.96 (09) nm to 0.89 (05) nm. Other radial integrals give different values. A possible discrepancy in the magnetic temperature scale for neodymium ethylsulfate is discussed.