I discuss the dependence of supersymmetric partition functions on continuous parameters for the flavour symmetry group. In the presence of the 't Hooft anomalies, the supersymmetric Ward identities imply that the partition function computed in the Wess-Zumino gauge has a non-holomorphic dependence on the flavour parameters. I show this explicitly for a large class of 4d N=1 partition functions on half-BPS four manifolds. I propose a new expression for the partition functions on M3 x S1, which differs from earlier holomorphic results by a non-holomorphic Casimir pre-factor.