After learning hard lessons rebuilding foreign militaries over the past dozen years, the U.S. military is shifting strategy against the Islamic State, choosing to train a smaller number of Iraqi soldiers rather than trying to stand up an entire army anew.

At their peak, Iraqi combat forces, painstakingly built and paid for by the United States during the last Iraq war, numbered about 400,000 troops. By the time the Islamist militant group launched its advance across northern Iraq in June, the Iraqi forces had shrunk by as much as half, depleted by years of corruption, absenteeism and decay.

When the Islamic State completed its seizure of the city of Mosul, four Iraqi army divisions and another from the federal police had disappeared, shrinking the original combat force to as few as 85,000 active troops, according to expert estimates. […]