Using the OPAL detector at LEP, the running of the effective QED
coupling alpha(t) is measured for space-like momentum transfer from the
angular distribution of small-angle Bhabha scattering.  In an almost
ideal QED framework, with very favourable experimental conditions, we
obtain:

   Delta[alpha(-6.07 GeV^2)] - Delta[alpha(-1.81 GeV^2)] = 
   (440 +- 58 +- 43 +- 30) *  10^{-5},

where the first error is statistical, the second is the experimental
systematic and the third is the theoretical uncertainty. This agrees
with current evaluations of alpha(t). The null hypothesis that alpha
remains constant within the above interval of -t is excluded with a
significance above 5 sigma.  Similarly, our results are inconsistent
at the level of 3 sigma with the hypothesis that only leptonic loops
contribute to the running. This is currently the most significant direct
measurement where the running alpha(t) is probed differentially
within the measured t range.