President Barack Obama could give final approval as early as Wednesday to expand the U.S. military contingent in Iraq, a source close to the discussions said, marking the first significant adjustment in his strategy since the insurgents seized Anbar’s capital Ramadi last month.

U.S. officials, speaking on condition of anonymity, expressed hope that a even a modestly beefed-up U.S. presence could help Iraq forces plan and carry out a counterattack to retake Ramadi.

But many critics have said previously that the current 3,100-strong American contingent of trainers and advisers is far from enough to turn the tide of battle.

Obama is expected to stick to his stance against sending American troops into combat or even close to the front lines, according to the officials, who spoke on condition of anonymity. But increased U.S. numbers in Iraq’s volatile Sunni heartland raises could mean running greater risks.

The proposed build-up comes as Obama’s anti-Islamic State policy faces mounting criticism at home and abroad. U.S.-backed Iraqi forces have made only halting progress against Islamic State militants who seized about a third of Iraq over the past year in a brutal campaign marked by mass killings and beheadings.

Obama said on Monday the United States did not yet have a “complete strategy” for training Iraqi security forces to reconquer land lost to Islamic State fighters.

Since the fall of Ramadi, which drew harsh U.S. criticism of the Iraqi military performance, Washington has begun to speed up supplies of weapons to the government forces and examine ways to improve the training program.

With Obama closing in on a decision, one U.S. official speaking on condition of anonymity said the increased U.S. deployment would likely entail several hundred more troops. A second official said the figure would be less than 500.

While it was unclear exactly how many would be deployed directly to Anbar, one U.S. official said many of those sent to the province would be stationed at a new training base there.

U.S. forces have already conducted training at the al-Asad military base in western Anbar.

Speculation on the location a new installation has focused on the area near the town of Habbaniya, the site of an Iraqi army base. A new site would allow U.S. forces to provide greater support for Sunni tribal fighters, who have yet to receive all of the backing and arms promised by the Shi’ite-led government in Baghdad.

“We are considering a range of options to accelerate the training and equipping of Iraqi security forces in order to support them in taking the fight to ISIL. Those options include sending additional trainers to Iraq,” said Alistair Baskey, a spokesman for the White House National Security Council. But he declined to provide details.

General Martin Dempsey, chairman of the Joint Chiefs of Staff, made clear during a visit to Jerusalem that there were no plans to fundamentally alter Obama’s military strategy that has so far kept U.S. ground troops off the front lines.

“We’ve made some recommendations on potential enhancements to the training and equip mission,” Dempsey said, citing options including new training sites.

Speaking to reporters traveling with him, Dempsey did not say how many extra U.S. troops may be involved. Another senior U.S. military official said only that the number would be modest.

At the Pentagon, spokesman Colonel Steve Warren said the United States had noted that forces in Iraq who had undergone U.S.-backed training emerged as “an improved fighting force.”

“Because of those observations, we’ve determined that it is better to train more Iraqi security forces and we’re now working through a strategy for how to do that,” Warren said.

The initial plan was to train about 9,000 Iraqi troops in a year. As of last Thursday, 8,920 Iraqi troops had received training at four different sites and another 2,601 were currently in some stage of training, he said.