WASHINGTON — The American job market improved modestly in October, and economists looking deeper into the numbers found real reasons for optimism — or at least what counts for optimism in this agonizingly slow economic recovery.

The nation added 80,000 jobs. That was fewer than the 100,000 that economists expected, but it was the 13th consecutive month of job gains. Fears of a new recession that loomed over the economy this summer have all but receded.

The unemployment rate nudged down, to 9 percent from 9.1 in September.

African-American unemployment fell slightly from 16.1 to 15 percent and in another encouraging sign black teen joblessness fell for the third straight month, moving from 44.2 percent to 37.8 percent.