NEW YORK (CNN/Money) - The Teamsters union and United Parcel Service are set to return to the negotiating table Tuesday with both sides expressing optimism that an early agreement can be reached.

Their contract does not expire until 12:01 a.m. Aug. 1, but an early agreement is necessary for UPS to stop customers from shifting business to competitors as protection against a possible work stoppage. Spokesmen for the union and company both say they're hoping an agreement can be reached by the end of this month or early July, rather than going to the 11th hour.

"If everything goes as we anticipate, certainly the end of June looks possible," union spokesman Brett Caldwell said. "We've made significant inroads on noneconomic issues. We anticipate continuing to make that progress. I think we'll have a better sense in the next couple of days."

Shares of UPS (UPS: up $0.33 to $62.20, Research, Estimates) gained Monday.

Company spokesman Norman Black said UPS has not yet seen any diversion of freight by customers, but the risk will increase as the deadline gets nearer.

"As we're talking today we haven't seen any diversions, but we're getting near to that point where the risk is much greater," Black said. "As you get closer to July, you'll have customers who remember what happened five years ago who were stranded without service making other arrangements."

The Teamsters struck UPS for 15 days in 1997, the union's first nationwide strike against its largest employer. The strike shut down the world's largest transportation company and wasn't resolved until the company dropped a demand for separate company pension funds rather than contributing to multi-employer union plans that make UPS responsible for the retirees of other trucking companies, many of which have gone out of business.

The company is not seen pushing the same demand on pensions this time, and the company has continued to post strong profits since 1997, helping to put it in position to meet union demands.

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UPS also faces shareholder pressure this time that it did not in 1997, when it was an privately-held employee-owned company. It also faces greater competition from FedEx Corp., which has added a lower-cost ground parcel service as well as traditional trucking companies to provide national coverage, giving it greater ability to compete for nervous UPS customers.

FedEx spokesman Jess Bunn confirmed Black's statement that there has been relatively little shift of freight up to now.

"Hard to tell when we'll see an increase," he said. "Five years ago we started seeing spikes in volume a couple of weeks before the deadline. This time we've got extra capacity. I think customers are understanding we have a little more capacity and may wait. But we're asking for commitments if they're planning on using us."

If the Teamsters do strike UPS, many of the 13.6 million packages and documents it delivers daily will be grounded as no competitor has the capacity to handle that much volume. The company handles about 5 percent of the nation's gross domestic product in its trucks.

More than 200,000 Teamsters work at UPS, making it by far the union's largest employer. The union's membership working for other trucking companies decline due to bankruptcies of many union carriers. It has not succeeded in its effort to organize employees at FedEx, and a strike against a trucking company it is trying to organize, Union Pacific Corp. subsidiary Overnite Transportation, has dragged on for more than two years, with no end in sight.