Thanks to last-minute panic-hiring by federal agencies the highly touted job freeze President Carter slapped on the bureaucracy last winter is just now beginning to show results via a slimmed-down government.

Indeed, thanks to some fancy footwork by both political and career federal brass, U.S. employment actually went up nearly 6,000 bodies in the two months immediately following Carter's limited no-hire order.

The extra bodies were added to the federal establishment because word of a possible freeze hit the Washington rumor mill weeks before the Carter administration pushed the "stop" button on the federal hiring machine. By then between 5,000 and 6,000 "committment letters" had been written by officials, promising would-be workers jobs before Carter could shut the hiring door.

Government agencies hire 250,000 people a year. To trim back the size of the federal population, Carter ordered -- in mid-March -- a limited freeze on hiring. Under his plan agencies could hire only one replacement for every two workers who left, retired or died.

The only problem with his limited freeze order of March 14 was that it had been anticipated long days before by federal officials who were determined to beat it.

On March 2, for example, this column led with the item: "Key federal officials -- especially political appointees -- spent a lot of time last week writing committment letters."

The letters, the column said, "are not part of some romantic revival by the Carter administration. Rather, it is a pragmatic attempt to get in under the wire, to be 'home free' in case the president slaps a freeze on government hiring or promotions." Twelve days later the president did announce his hiring freeze.

Although Carter made the freeze retroactive to Feb. 29 -- that is the one-for-two hiring ratio was based on job vacancies as of that date -- the bureaucracy had partially out-foxed the president. More than 6,000 commitment letters -- official promises of a federal job -- were zipped off to prospective civil servants, and postmarked so as to beat the freeze.

Because of the commitment letters, which agencies had to honor, federal employment last spring actually jumped about 6,000 persons despite the freeze. The number of full-time permanent employes began to drop in May, and officials think the first full month's impact of the partial freeze will show up when June employment figures come out.

Because the freeze has been slow to take effect, it is a good bet that Carter will keep it on most agencies until the elections are over. That way he can tell the nation's voters, before they go to the polls, that he has succeeded in cutting back the size of the bureaucracy.

Freeze Effects: Very few federal officials like job freezes. Most think a freeze is 90 percent public relations and 10 percent had business.

They argue that hiring freezes slow the normal rate of attrition, causing older workers who would normally retire to hang on longer until things get better and the freeze is lifted.