Magnetostatic wave - optical interactions are studied in the transverse geometry using a [BiLu]3Fe5O12 film. Non-monotonic variations in the magneto - optic coupling coefficient are observed as we increase the input microwave power at a fixed frequency. Similar variations are also seen in the transmitted microwave signal, though the features appear at higher power levels. The non-monotonic behavior is due to a shift in the microwave passband with increasing power. Density plots are used to correlate the two sets of data over a 350 MHz region. The discrepancy in power levels associated with a feature in the line plots is a consequence of the different curvatures of the two density plots.