Fresh from the success of its War on Rats, the D.C. Department of Environmental Services has declared a War on Cockroaches.

The War on Rats was conducted with pamphlets, mobile teaching units, posters and a separate telephone listing. It taught the little critters a lesson, and if you see a furry animal scurrying along the alley, it must be somebody's pet hamster out for some fresh air.

Cockroaches are going to be harder. They are too small to get a full view of threatening posters, and are easily outdistanced by a mobile unit because while no one can beat their time at running behind the stove, their legs are very short.

Nevertheless, we now have seasoned troops. We have sophisticated techniques of psychological warfare which have been applied with equal success to rats and foreigners. This time, we are going to win.

The key to the solution appeared in the very declaration of war. "We're getting the complaints from all parts of the city," said the service's director. "Heretofore the complaints have been from tenants in substandard apartment buildings, but now we're getting them from single-family homes and all areas."

As this makes clear, the problem with cockroaches has traditionally been that they are associated with substandard living. A roach crawling across your kitchen counter implied poverty and uncleanliness, even if the counter is butcher block and he's moving along to investigate what is in the Cuisinart.

Anybody who has ever tried to hit, spray or scream a cockroach out of existence knows how impossible that is.

We're not going to change the cockroaches, but in the great American tradition of adjusting to an evil, rather than remedying it, we can change our attitude. Cockroaches indeed are no respecters of wealth. Once we convince people that their presence is no reflection on the income or personal habits of the host, we will have won the war.

It has been done with head lice. The reputation lice had for hanging around with undesirables made the recent epidemics frightening, until the problem was solved by the simple expedient of introducing lice into the private schools. Now if your child is lousy everybody knows it cost you $2,500 a year to get him that way.

As cockroaches are identified with the high-rent districts, they will no longer inspire fear and loathing. We will have won at least a moral victory. And besides, they might get disgusted then, and go away.