When the presidents of Mexico and the United States sit down together at the White House tomorrow, high on their agenda will be the complex, sensitive issue of U.S. immigration policy. t

This great human problem is made far worse than it has to be by the ministrations of a ponderous bureaucracy that manages to be arbitrary, slipshod and wasteful all at the same time.

Of course, Mexican President Jose Lopez Portillo may not even realize that this is a problem. What he does realize is that the money earned and sent back to their families by Mexican immigrants is important to Mexico's economy. And he is also aware that the Immigration and Naturalization Service spends an inordinate amount of time and effort rounding up illegal immigrants and dumping them back over the border.

It probably puzzles him that most of those who are deported are not criminals or welfare leeches, but hard workers who are careful to stay out of trouble. He must wonder why the very kind of penniless immigrants whose hard work made this nation what it is are not greeted with a welcome mat instead of barbed wire.

Part of the immigration agency's problem may well be that its employees themselves are a little uncertain of the justice of their assignment. They may feel guilty about having to track down people whose only real crime is to want a better life for themselves and their children.

An immigration official once told me about an old man who packed all his worldly goods in a knapsack and trudged across 200 miles of Mexican desert to sneak into Arizona. He was caught and sent back; then he did it all over and was caught again -- four times in all. The official wondered if such persistence shouldn't somehow have entitled the old man to say in the United States.

The official also recalled an INS raid early one morning on a ranch where illegal aliens were believed to be employed. The agents found several American workers warming themselves around charcoal burners; the aliens were out in the fields hard at work. "I felt that we were deporting the wrong people," the official told me.

Whether or not uncertainty over their role has sapped morale at INS, the fact remains that few federal agencies can match the immigration service in inefficiency and waste.

The president's Management Improvement Council spent last year checking the immigration agency's procedures, practices and budget. Some of their findings are still confidential, but my associate Lucette Lagnado interviewed council officials and studied page after page of documents prepared by its investigators. Here is some of what they learned:

Massive overtime raked in by INS inspectors has reached critical proportions. A 1931 law requires that federal employees who work beyond "normal" hours be given generous overtime pay. Because planes and ships arrive at odd times -- the illegal aliens rarely try to cross the border between 9 a.m. and 5 p.m. -- the INS overtime budget is astonishing.

The White House investigators discovered that several agency employees were making as much as $40,000 a year over and above their regular salaries. Even though a limit on individual overtime has been decreed recently, the agency's overtime budget is likely to be more than $20 million this year.

This lucrative overtime has led to another problem: many employees resist promotions that would eliminate their overtime pay, thus depriving the service of some of its most experienced people in management positions.

"Symptoms of organizational illness" and "lack of stability" in top management have led to internal bickering and confusion. The turnover has been astounding: in the three years ending last December, efficiency experts found that 131 of 263 top administrative officials had been transferred -- a 50 percent turnover.

Morale seems low. Investigators found a definite and widespread tendency among employees to complain that the agency is underfunded and understaffed.

The immigration service has lagged behind other federal agencies in modernizing its management techniques. For example, though INS has literally millions of individual dossiers, it lacks a proper computer system to keep track of them.

In addition, the service persists in sticking to its traditional "one-on-one" approach, pursuing each case on an individual basis. In some ways, of course, this is humane and commendable, but lack of statistical samplings, inspection profiles and other modern techniques means that the agency's allocation of personnel and funds is haphazard and inefficient. The White House management experts concluded sadly that "a quick fix of the INS is not possible."