  The Delta-variance analysis, has proven to be an efficient and accurate
method of characterising the power spectrum of interstellar turbulence. The
implementation presently in use, however, has several shortcomings.
  We propose and test an improved Delta-variance algorithm for two-dimensional
data sets, which is applicable to maps with variable error bars and which can
be quickly computed in Fourier space. We calibrate the spatial resolution of
the Delta-variance spectra.
  The new Delta-variance algorithm is based on an appropriate filtering of the
data in Fourier space. It allows us to distinguish the influence of variable
noise from the actual small-scale structure in the maps and it helps for
dealing with the boundary problem in non-periodic and/or irregularly bounded
maps. We try several wavelets and test their spatial sensitivity using
artificial maps with well known structure sizes.
  It turns out that different wavelets show different strengths with respect to
detecting characteristic structures and spectral indices, i.e. different
aspects of map structures. As a reasonable universal compromise for the optimum
Delta-variance filter, we propose the Mexican-hat filter with a ratio between
the diameters of the core and the annulus of 1.5.
