This paper describes the use of a high resolution beta-ray spectrometer ( Δp/ p ∼ 0.1%) to measure short lifetimes in nuclei recoiling from nuclear reactions or alpha decay. The method takes advantage of the Doppler shift in the momentum given to electrons emerging from recoiling atoms which is ≥ 0.1% following alpha decay and ≥ 1% for typical heavy ion reactions. The 42.8 keV transition in Pu 240 following alpha decay of Cm 244 was studied in detail as an illustrative example; the L II and L III conversion lines from an uncovered Cm 244 source are shown to have the expected Doppler structure in the form of high momentum shoulders extending ∼0.3% above the unshifted momentum p 0 of electrons emerging from atoms at rest in the source backing. With use of an electrode system of two grids placed close to the source so that the electrons are first decelerated and then reaccelerated it is shown that the electrons emitted from recoiling atoms can be given a net acceleration which is proportional to the distance travelled by the atom from the source surface before electron emission takes place. The L III 42.8 line has been studied directly and also in coincidence with alpha particles detected behind the source, with applied electric fields of up to 40 000 volt/cm. Analysis of the resulting line shapes yields a halflife of (1.6 ± 0.2) × 10 −10 sec, without correction for absorption in the source (which would tend to raise the value). A value of (1.72 ± 0.15) × 10 −10 sec has been measured electronically by Bell et al. A discussion of the potentialities of the method shows that it should be possible to measure lifetimes as short as ∼ 3×10 −12 sec following alpha decay and as short as 3 × 10 −13 sec following reactions involving heavy ions.