The Paris attacks and the downing of a Russian airliner have heightened determination in Moscow, Paris and Washington to defeat Islamic State, a challenge easier said than done.

Many strategists say military advances will show little progress unless more work is done to eliminate the militant group’s financing, counter its propaganda and cut a diplomatic deal among world powers on Syrian rule.

For military planners, destroying the terrorist group’s headquarters and crippling its fighting force is a relatively simple assignment, say strategists: It would require some 40,000 troops, air support and two months of fighting.

The problem is what do to after taking responsibility for won territory. With the recent experience of Afghanistan and Iraq, that is a job no Western leader wants. Many officials, especially in Europe, believe a full-scale military response would help Islamic State, also known as ISIS and ISIL, by broadcasting an image of Westerners seizing Arab lands, attracting more followers to the militants’ cause.

“Drawing us into a ground war with them is a trap,” said a French government official. “Frankly, I doubt it would go very well.”