In this paper a compound rotation-invariant filtering technique is developed which leads to sharp cross-correlation peaks for desired targets, while suppressing random noise and unwanted target correlations. The basic compound filter structure consists of a weighted sum of the cross-correlations between several circular harmonic filters (CHF's) and the input image. In the design procedure, the weights are constrained so that the compound filter output has a peak value of 1, for the desired target. Measures of random noise, and deterministic noise due to correlations with unwanted targets, are minimized with respect to the weights. The signal-to-noise ratio (SNR) of the compound filter is therefore maximized. Some limits to the performance of the technique are discussed. The output magnitude squared cross-correlation functions form a non-orthogonal set of functions. Therefore, the SNR could be made arbitrarily large if the functions were linearly independent and a very large number of CHF's were available. Examples illustrating the filter performance are given. Extensions of this work are discussed.