"fell moderately" is a correct and usable phrase in written English.
You can use it when you are describing something, such as a temperature, declining from a high to a lower point, but not to the lowest point. For example, "The temperature fell moderately throughout the day."
Japanese stocks fell moderately early today.
As the dollar gained ground, gold prices fell moderately.
Crude oil prices for near-term delivery fell moderately on the New York Mercantile Exchange amid perceptions of slack demand.
Stocks fell moderately on Monday morning as talks stood at a standstill, but rose later as the mood improved.
Soybean futures prices fell moderately on the Chicago Board of Trade, reflecting expectations for heavy deliveries Monday against the January contract.
[C8.] Stocks Slide on Economic Data Stocks fell moderately as investors were discouraged by more weak economic data and a new wave of corporate earnings warnings.
Since that time both mortality and fertility rates have decreased, and the annual growth rate has fallen moderately, to about 1.7 percent.
The downturn in the housing market, it said, would brake the growth in consumption from 3.0% this year to 1.8% in 2005 the smallest increase since 1995.The forecast assumes that house prices will stabilise or fall moderately.
The irrigation suitability for EC values falls moderately to high saline whereas TDS values belong to fresh water class.
In another we assume that the areal share of crop types other than rice, wheat, coarse grains, and oil seeds in each country will fall moderately by 2015 when compared to 2000 levels (q = 3; Text S1 and Table S16).
Sales were falling off moderately, and inventories were growing, but not as fast as in other areas in the region.
