LONDON — In barely a generation, air power has shifted from indiscriminate to discriminating. Thanks to advances in precision guidance, American bombs and missiles now generally get to where they’re intended. But human or machine error, bad luck or faulty military math still lead to unforeseen civilian deaths. And as the United States and its allies continue their bombing campaign against the Islamic State in Iraq and Syria, many more noncombatants are perishing than they seem prepared to admit.

During July, the number of reported civilian casualties from coalition airstrikes reached the highest level since the air war began in August 2014. On July 19, 78 or more civilians were reported killed near the Islamic State-occupied city of Manbij, Syria, many of them women and children. In the successful battle for Manbij alone, at least 200 civilians were reportedly killed.

The United States and its allies have taken care to mitigate harm to civilians, and the United States Central Command is investigating the July 19 incident. But with the fight moving deeper into the towns and cities of Iraq and Syria — where millions remain under the Islamic State’s thumb — the risk is rising. Denmark, a member of the coalition, recently warned that civilian deaths might be “unavoidable” in this new phase of the war. Yet the allies appear poorly equipped to properly assess the numbers already being killed.

Airwars, the organization I lead, at present estimates that at least 1,500 civilians have been killed by the United States-led coalition — around one death for every nine strikes. Similar or higher tallies are reported by other monitoring groups, like Iraq Body Count and the Syrian Observatory for Human Rights. But coalition officials have publicly admitted just 55 deaths. At a Pentagon briefing in April, Maj. Gen. Peter Gersten dismissed as “propaganda” significant assertions to the contrary, telling reporters he had “a high level of confidence” in official casualty investigations. Can the coalition’s assessments really miss 95 percent of fatalities in Iraq and Syria?