The state's seasonally adjusted jobless rate dropped a tenth of a point last month, to 8.2 percent.
Figures from the Department of Administration show Arizona added 30,000 jobs between August and September. Most of those, however, were workers returning to jobs in public schools, community colleges and state universities.
But Aruna Murthy, the agency's director of economic analysis, said the state also added 5,200 jobs in the private sector. That puts private employment now 53,300 higher than a year ago.
Murthy acknowledged there was a steeper decline in the national unemployment rate. It went down 0.3 percentage points, to 7.8 percent.
She said, though, that national trend appears to be largely a function of unemployed people finding part-time work -- and therefore being counted as employed -- rather than getting full-time jobs.
Big gainers in Arizona last month include the health care industry, with a sharp hike in employment at medical offices.
Several sectors of the economy posted losses, including construction which shed 1,200 jobs between August and September, with 1,600 jobs lost in retail trade. Murthy said that latter figure appears to reflect layoffs of temporary workers who were previously hired for the back-to-school shopping season.
One area of the economy that is lagging is private sector education. And that was even before this week's announcement by University of Phoenix that it was closing some of its sites and laying off workers.
Murthy said some of what is happening appears to be due to tighter federal regulations on student loans for these private colleges.
"But the other side could be the economy's slightly improving,'' she said.
"So the likelihood of you finding a job is greater than what you had two years ago,'' Murthy continued. "So as the economy improves, generally people tend to want to go and work rather than go back to school.''
Overall, Murthy said the state's economy continues to improve at a decent pace.
She said that year-over-year job growth so far in 2012 is running above 2 percent. And the last time the annual increase was running that high was in early 2007.