We present complete axiomatizations of weak hypercongruence in the finite fragment of the fusion calculus, an extension and simplification of the pi-calculus. We treat both the full fusion calculus and the subcalculus without mismatch operators. The axiomatizations are obtained from the laws for hyperequivalence and adding so called tau-laws. These are similar to the well known tau-laws for CCS and the pi-calculus, but there is an interesting difference which highlights an aspect of the higher expressive power of the fusion calculus.