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The phrase "a further reduction in" is correct and usable in written English.
It can be used when discussing a decrease in quantity, size, or intensity, often in a formal or technical context.
Example: "The report indicates a further reduction in emissions over the next five years."
Alternatives: "an additional decrease in" or "a continued decline in".
Exact(59)
"This will result in a further reduction in our yields".
A further reduction in the top rate of tax.
There is scope for a further reduction in interest rates.
"Sanctions will mean a further reduction in standards of living and fewer resources for the people.
There was no serious discussion of a further reduction in the Bank rate.
This may entail troop cuts and a further reduction in army patrols.
Warren Lasko, executive vice president of the association, predicted a further reduction in foreclosures.
Among ideas likely to worry Britain, Belgium suggests a further reduction in policy areas subject to national vetoes.
However, a dose of 6 g of β-glucans did not result in a further reduction in serum cholesterol concentrations.
However, it is important to note that a further reduction in policy rates are not automatic.
For all test problems, the cuts yield a further reduction in the solution time.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com