The 30-minute promise for telephone orders had been in effect since 1984, serving as the backbone of Domino's rapid growth into the largest pizza-delivery company in the country. Until 1986, a late-arriving pizza was left at no cost to the customer. Since then, customers have been given $3 off their orders.

While the pizza deliverers have been the source of the company's legal problems, Domino's executives said the key to meeting the 30-minute promise was how quickly the orders were taken, pizzas were made and orders were completed. No Penalty for Lateness

As the anchor leg of the relay team, the delivery person was never charged by the company for late deliveries, said Tim McIntyre, a spokesman for the company, which is based in Ann Arbor, Mich. In fact, any pizza that had not left the store within 25 minutes of the placement of the order was automatically marked "late," he said, and delivered with the appropriate price adjustment.

In the latest of a series of lawsuits against the privately owned company, Jean Kinder, a 49-year-old St. Louis woman, suffered head and spinal injuries when a Domino's delivery driver ran a red light and struck her car. The Missouri circuit court jury on Friday ordered the company and the local franchise operator involved to pay her $750,000 in actual damages, and $78 million in punitive damages.

The change in policy by Domino's could have a profound impact on the way the company does business, and ultimately on its sales. Unlike Pizza Hut, a subsidiary of Pepsico Inc. that operates 4,443 carry-out units among its 7,800 United States restaurants, Domino's depends largely on delivery services. The company said it expected to report about $2.3 billion in sales this year. Rivals Could Benefit

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While it periodically altered or expanded its menu, Domino's biggest selling point was speed of delivery, aided in recent years by computer listings of customers by phone numbers, to track their names, addresses and preferences for regular pizza or thin-crusted, green olives or black, diet cola or regular.

The difference between ringing the doorbell within 30 minutes instead of, perhaps, within 35 may sound small. Marketing experts contend, however, that canceling the guarantee may send consumers to other pizza delivery companies, like Little Caesars, or to neighborhood Chinese restaurants.

"It's one of those things that is difficult to define," George Thompson, a restaurant chain analyst with Prudential Securities, said of the potential impact on Domino's sales. "But the point is, it's not great. With a major competitor like Pizza Hut, where the quality is very good, service becomes an important factor. With Domino's, the fact they built their business by delivering in a timely fashion is also important. Now they will not be able to deliver so timely.

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"In general," Mr. Thompson added, "that could be a negative perception."

A negative perception might also be building as a result of the lawsuits against Domino's for accidents involving delivery people, all of whom use their personal means of conveyance for the job. Suits and Settlements

In May, the company agreed to a settlement of $2.8 million with the family of Susan Wauchop, a 41-year-old woman from Calumet City, Ill., who was struck and killed in her van three years earlier by a Domino's delivery driver. The plaintiffs charged that the driver was negligent in trying to arrive within the promised time.

In August, Matthew D. Jacks, a 19-year-old man from Lewiston, Me., sued Domino's, contending he was struck by a driver in March, causing injuries to his pelvis, knee and thumb.

Other cases, including one six months ago in West Virginia, ended in Domino's favor when the plaintiffs' claims against the company were rejected.

Despite the scores of lawsuits against the company since the 1980's, Mr. Monaghan, the sole owner of Domino's, took issue with the notion that the accidents might reflect the possibility that the company had relaxed its emphasis on safety.

"Domino's has always been committed to safety," he said in a statement issued by the company. "But there continues to be a perception -- a perception I believe is not supported by the facts -- that the guarantee is unsafe. We got that message loud and clear. So, we are eliminating the element that creates that negative perception."