  We investigate the power of wavelet techniques in detecting non-Gaussianity
in the cosmic microwave background (CMB). We use the method to discriminate
between an inflationary and a cosmic strings model using small simulated
patches of the sky. We show the importance of the choice of a good test
statistic in order to optimise the discriminating power of the wavelet
technique. In particular, we construct the Fisher discriminant function, which
combines all the information available in the different wavelet scales. We also
compare the performance of different decomposition schemes and wavelet bases.
For our case, we find that the Mallat and {\it \`a trous} algorithms are
superior to the 2D-tensor wavelets. Using this technique, the inflationary and
strings models are clearly distinguished even in the presence of a superposed
Gaussian component with twice the rms amplitude of the original cosmic string
map.
