  We show how to determine the lowest order mixing of all scalar with
two-fermion two impurity BMN operators in the antisymmetric representation of
SO(4). Differentiation on harmonic superspace allows one to derive two-loop
anomalous dimensions of gauge invariant operators from this knowledge: the
value for the second anomalous correction to the dimension is essentially the
square of the two-fermion admixture. The method effectively increases the loop
order by one. For low J we find agreement to all orders in N with results
obtained upon diagonalisation of the N=4 dilation operator.
  We give a formula for the generalised Konishi anomaly and display its role in
the mixing. For J=2 we resolve the mixing up to order $g^2$ in the singlet
representation. The sum of the anomaly and the naive variation of the leading
two-fermion admixtures to the singlets is exactly equal to the two-fermion
terms in the antisymmetric descendants.
