Some economic series in small economies exhibit meager (i.e., non-positive) values, as well as seasonal extremes. For example, agricultural variables in countries with a distinct growing season may exhibit both of these features. Multiplicative seasonal adjustment typically utilizes a logarithmic transformation, but the meager values make this impossible, while the extremes engender huge distortions that render seasonal adjustments unacceptable. To account for these features we propose a new method of extreme-value adjustment based on the maximum entropy principle, which results in replacement of the meager values and extremes by optimal projections that utilize information from the available time series dynamics. This facilitates multiplicative seasonal adjustment. The method is illustrated on New Zealand agricultural series.