The phrase "a steady reduction in" is correct and usable in written English.
You can use it when discussing a consistent or gradual decrease in a particular quantity or measure over time.
Example: "The company has reported a steady reduction in production costs over the last quarter."
Alternatives: "a gradual decrease in" or "a consistent decline in".
Over the past decade, Kazakhs have experienced a steady reduction in individual rights.
Nationally, there has been a steady reduction in the daily population at detention centers.
There has been a steady reduction in car-train fatalities in the country.
But from the Middle Ages to modern times, we can see a steady reduction in socially sanctioned forms of violence.
One of the cardinal features of semantic dementia (SD) is a steady reduction in expressive vocabulary.
Moreover, political infighting hampers the ability of the government to achieve a steady reduction in the budget deficit.
In 2004, the Ministry of Health reported a steady reduction of anaemia prevalence in Balkan and Dashoguz Velayats, where a multi-component Anaemia Prevention and Control Programme supported by UNICEF has been implemented since 1998.
It's true that the internet has led to a sharp, steady reduction in letter volumes – down 2% in the most recent figures.
From the mid-1950s to around the late 80s, there was a fairly steady reduction in the proportion of total British exports and imports flowing to and from the Commonwealth.
The wars fought by members of the Hauteville family contributed to a steady reduction of Muslim and Byzantine power in the region.
Although we found it difficult to analyze for the effect of delayed treatment on new AIDS-defining diagnoses, we report a slow but steady reduction in overall new clinical events at increasing baseline CD4 counts during the observational period, although no statistical differences were detected between the two groups.
