When Bob Connelly decided to sell an electronic mousetrap in Japan two years ago, the Japanese did not exactly beat a path to this door.

In fact, they never got the chance. Connelly, who runs a small, Tokyo-based marketing firm for American products, had to abandon the idea as too costly after learning of Japanese government regulations that would have required him, in effect, to replace the electrical cords on the inexpensive, American-made devices with ones made in Japan before they could be sold here.

Connelly had been caught, he said in a recent interview, in the "non-tariff barrier" (NTB) trap, the web of customs, product standards and testing procedures that foreign businessmen frequently complain keep them from successfully marketing products in Japan.

Under mounting U.S. pressure to open the market here or face protectionist action, the Japanese leadership is moving to cut through the bureaucratic barbed-wire that has hampered imports by relaxing or eliminating some trade barriers and promising action on other complaints from trading partners.

But progress on the issue is apt to be piecemeal and far too slow to satisfy the country's U.S. and European critics, who say the package falls far short of meeting demands for fair market access and complain that the measures break little new ground.

No one, including the Japanese, seriously expects the new measures to put much of a dent in the huge U.S. trade deficit with Japan, which is projected to top a record $20 billion this year.

"If all the barriers were dropped by Japan," Lawrence F. Snowden, president of the American Chamber of Commerce in Tokyo, told reporters here last week, " that is not going to solve the fundamental trade imbalance problem. What it will do is take the political heat out of the trade question."

It may not succeed in doing even that.

The package that Prime Minister Zenko Suzuki's Cabinet adopted late last month is designed to relax or eliminate 67 non-tariff barriers compiled from a list of 99 specific complaints brought by major trading partners.

Tokyo has promised prompt action on nine more complaints and set up a governmental Office of Trade Ombudsman comprised of top officials from each Japanese ministry and a working-level staff to deal quickly with gripes on market access raised by foreign entrepreneurs.

Tokyo's latest round of measures reflects a growing concern among senior officials and politicians here that key overseas markets for the country's export-led economy could start snapping shut unless they move quickly to alter the widespread perception of Japan as a closed market.

But some American businessmen and U.S. officials in Tokyo point out that a number of the 67 items on the list already have been acted on in recent years.

For example, the Ministry of Transport has promised to ease rulings in nine areas governing automobile imports by dispatching customs inspectors to plants abroad, accepting test results conducted by foreign officials and delaying the enforcement of strict new exhaust-emission standards. But ministry officials acknowledged that these provisions have been largely in effect for the past five or six years and now simply will be broadened in scope.

The Cabinet's package also does not, for instance, address the issues of opening Japan to more service industries such as banking and insurance or expanded imports of big-ticket telecommunications or data-processing equipment.

It also leaves aside the question of Japan's 22 quotas on agricultural products, which Tokyo has used to protect its cloistered farm sector.

The Ministry of Agriculture has strongly opposed any significant concessions on the non-tariff barriers and the ruling Liberal Democratic Party, which counts heavily on the support of the country's farming communities, has shied away from pressing the matter.

"You may think the package is rather conservative," said Akinori Marumo of the newly established ombudsman's office. "But we've tried very hard in the last two or three months to push the ministries concerned to accept as much as possible. Other large items will also be tackled, but it takes time."

"These are not stalling tactics," one U.S. official in Tokyo said. "The Japanese are now trying to grapple with the internal political struggles that are inherent in solving NTB problems within the bureaucracy."

What is significant about these efforts, he said, is that "the Japanese are finally willing to look at the complaints of foreign businessmen," which they have frequently brushed aside in the past on the grounds that foreigners have not, as a rule, made determined enough efforts to break into the market.

In perhaps the most significant departure, meanwhile, Tokyo has pledged to adopt a more streamlined system for customs procedures, including the simplification of import documentation and a relaxation of inspections of goods that have, in the past, caused lengthy delays (frequently two to three months) in getting shipments cleared for entry into the market.

And while a number of the specific barriers to be lifted deal with only one product often produced by a single foreign company, they appeared to point to a greater acceptance by the Japanese of foreign testing standards and data. That could led to import approval for a broad range of goods, including pharmaceuticals, cosmetics, electrical appliances and sophisticated medical equipment.

Nevertheless, plenty of trade bottlenecks remain that the recent rulings are not likely to touch, according to foreign businessmen here. Among them is the customs officials' practice of handing over potential import products to private Japanese for standards testing because of the lack of government-run laboratory facilities.

"In many cases," said one American businessman in Tokyo, "products are inspected by direct Japanese competitors and the importer often has no idea because it's done under the umbrella of an 'independent' testing group."

In other cases, the U.S. official said, foreign products face "non-mandatory" standards set by Japanese industry associations, which issue a "safety" certification without which products are difficult to market.

During the recent roller-skating craze that the Japanese imported from the United States, for instance, American-made roller skates were effectively kept out, he said, because only Japanese manufacturers could meet the standards.