  The advantages of weak measurements, and especially measurements of imaginary
weak values, for precision enhancement, are discussed. A situation is
considered in which the initial state of the measurement device varies randomly
on each run, and is shown to be in fact beneficial when imaginary weak values
are used. The result is supported by numerical calculation and also provides an
explanation for the reduction of technical noise in some recent experimental
results. A connection to quantum metrology formalism is made.
