Federal prosecutors thought that they had all the elements of a strong insider-trading case against former presidential adviser Thomas C. Reed: incriminating telephone records, backdated documents, proceeds going to his girlfriends.

But they had no evidence of what went on during two crucial phone calls, lasting 10 minutes. Prosecutors argued that, during those conversations, Reed had obtained secret information from his father, a corporate director. The two men denied it.

Reed's acquittal by a federal jury in Manhattan last month was more than a personal vindication for the former Air Force secretary.

It was a reminder to government investigators and prosecutors that, although purely circumstantial evidence may produce indictments, winning convictions in a courtroom can be tricky. In fact, many defendants negotiate plea bargains and few are brought to trial, in part because it is difficult to win such cases without some sort of "smoking gun," or incontrovertible evidence.

Albert Culler, a Reed case juror, said after the trial that prosecutors had failed to prove beyond a reasonable doubt that Reed received insider information from his father. "They could have done a better job," Culler said of the prosecutors.

"You can have as much circumstantial evidence as you can get, but in dealing with people who have impeccable reputations, it's very important to get someone from the inside to cooperate," said Charles P. Roistacher, an assistant U.S. attorney here who prosecuted former deputy defense secretary Paul Thayer. There was no such witness in the Reed case.

Speaking of insider trading generally, Roistacher said: "People get away with it when they limit the trading to extremely loyal friends . . . . If they disguise it real well and keep it within a small group of people, it's very difficult to detect."

Ira Lee Sorkin, head of the Securities and Exchange Commission's New York office, said the SEC cannot catch everyone who trades on inside information. He said such cases "are difficult to prove because it's extremely difficult to find the source of the leak."

"You may find out that the guy who bought a lot of stock the day before a merger announcement happens to be the golfing partner of the chairman of the board, but both deny they discussed the case," Sorkin said. "Where do you go from there?"

The SEC brought 20 such cases last year, based on 200 complaints, and is currently investigating another 50. The record-breaking wave of corporate takeover attempts, which tend to boost the stock of the company being acquired, has greatly increased the opportunities for quick, illegal profits.

The SEC settles many such cases with civil consent decrees, in which the defendant admits no wrongdoing but agrees to repay profits from the disputed stock transaction. A 1984 law also enables the SEC to recover triple damages in some circumstances.

Michael R. Klein, a Washington securities lawyer, said the SEC is "terribly understaffed" and that the odds of getting away with an inside stock deal "are at least 10 to 1."

"The problem is rampant, epidemic . . . . Almost invariably, things like bankruptcies, takeovers and large government contracts are preceded by active trading in which people make a whole lot of money," Klein said.

The law does not precisely define insider trading; the SEC has continually tried to expand the law to cover anyone who knowingly trades on confidential information not available to the general public.

But Klein said that a string of Supreme Court rulings over the last decade has "severely constrained the reach of existing laws." He said this has forced investigators to prove that the insider was breaching his fiduciary duty in passing on the information, or that the recipient of the tip was aware of this.

"They have to prove much more, and some things are no longer violations even if they can prove them," Klein said.

That approach has its pitfalls. Several years ago the Supreme Court ruled that a printer, Vincent Chiarella, broke no law by trading on corporate information that he gained by printing a company's reports. In 1983, the court acquitted a whistle-blowing analyst, Raymond L. Dirks, who told his clients about a massive securities scam -- enabling them to sell -- before alerting the SEC.

On the other hand, prosecutors won convictions against a typist for a New York law firm specializing in mergers, and against former Wall Street Journal reporter R. Foster Winans, who leaked advance information from his stock market column. They argued in both cases that the defendants had breached their fiduciary duty to their employers or stockholders.

But how far do those responsibilities extend? To a financier who is approached about backing a takeover attempt? To a television station employe who knows that an unfavorable show about a prominent product is about to be aired? To a small investor who gets an inside tip third-hand? SEC officials have resisted attempts to clarify the law, saying they do not want to spell out in advance which conduct is prohibited.

No one faced criminal charges for insider trading before 1978, but such cases are increasingly referred for prosecution, especially when the defendant is accused of lying to the SEC.

The U.S. attorney's office in Manhattan, where the major stock exchanges are located, rarely loses an insider-trading case, in part because weaker cases are declined or are settled without criminal charges. The office has won convictions against 41 persons on insider-trading charges since 1982.

The cases were so strong that most defendants pleaded guilty; they ranged from lawyers, bankers and stockbrokers to policemen, cabdrivers and receptionists. Reed was the only one to win acquittal in that period.

The Reed case began in 1981, when the California businessman turned a $3,000 investment in Amax Corp. stock options into a $431,000 profit in two days. He settled SEC civil charges by repaying the money, then was indicted for fraud and obstruction of justice last year.

Reed bought the options immediately after the two phone conversations with his father, an Amax director, who had been summoned to a board meeting to consider a merger offer from Standard Oil of California. Reed sold his options after the takeover attempt sent the price of Amax stock soaring.

Reed and his father denied discussing the takeover attempt. Reed said he had bought the options for friends and associates and backdated documents and forged signatures so they could receive the proceeds.

Reed's lawyer, Edward Shaw, argued that it was logical for Reed to invest in his father's firm and that Reed made extensive notes on the investment because he regarded it as a gamble. Shaw also called as witnesses several prominent officials who praised Reed's integrity.

"The government had no direct evidence," said Charles M. Carberry, the assistant U.S. attorney who handled the case. "We had no accomplice as a witness. Our evidence consisted basically of the telephone records showing the timing of the calls and the purchases that quickly followed.

"It comes down to circumstantial evidence," he said. "It comes down to the credibility of the witness." To reach a guilty verdict, he said, "The jury has to decide that the defendant . . . is a liar."

A different strategy emerged in the insider-trading case involving Thayer, who is a friend of Reed. Thayer pleaded guilty in May to obstruction of justice and was sentenced to four years in prison.

Thayer initially denied leaking information about companies of which he was a director to his girlfriend and seven other associates, who reaped $2 million in illegal profits. But prosecutors persuaded the girlfriend, Sandra K. Ryno, to cooperate with the government, thereby learning of secret phone calls that Thayer made to her, his stockbroker and others by using a friend's credit card.

"If Paul Thayer had gone to trial and we had only circumstantial evidence -- dealing with a deputy secretary of defense, a war hero with every honor in the book -- it would have been tough," Roistacher said.

No matter what investigators do, Klein said, "You can never stop it all. What you can do is have a credible deterrent. It's sort of like income tax evasion; the IRS has established a fear of prosecution. The SEC has failed to establish that, notwithstanding four or five years of rhetoric."