A survey of parity-changing $E1$ transitions has been pursued in $N\ensuremath{\gtrsim}Z$ nuclei near $^{56}\mathrm{Ni}$ using data from an EUROBALL experiment. Linear polarization measurements have been combined with angular correlations of coincident $\ensuremath{\gamma}$ rays to determine the electromagnetic character of numerous transitions. The impact of the results on shell-model parametrizations is briefly discussed.