  The backwards diffusion equation is one of the classical ill-posed inverse
problems, related to a wide range of applications, and has been extensively
studied over the last 50 years. One of the first methods was that of {\it
quasireversibility\/} whereby the parabolic operator is replaced by a
differential operator for which the backwards problem in time is well posed.
This is in fact the direction we will take but will do so with a nonlocal
operator; an equation of fractional order in time for which the backwards
problem is known to be ``almost well posed.''
  We shall look at various possible options and strategies but our conclusion
for the best of these will exploit the linearity of the problem to break the
inversion into distinct frequency bands and to use a different fractional order
for each. The fractional exponents will be chosen using the discrepancy
principle under the assumption we have an estimate of the noise level in the
data. An analysis of the method is provided as are some illustrative numerical
examples.
