Before Preet Bharara became the United States attorney for the Southern District of New York, insider trading cases almost always singled out amateur, unsophisticated investors. That was because of the way such cases were usually uncovered. After some news — of a takeover, perhaps, or an earnings collapse — caused a big stock swing, investigators looked for trades that seemed to have been prescient.

Image Judge Richard Sullivan’s instructions to the jury were challenged on appeal. Credit... U.S. District Court, SDNY

If the investigation found someone who rarely traded stocks but made a killing on one trade, suspicions were aroused. If it turned out that investor knew a corporate insider, and that phone records showed the two talked just before the suspicious trades, the trader faced questions.

A typical civil insider trading case was announced by the Securities and Exchange Commission the day before the appeals court heard the fund managers’ appeal. That case involved an official of a small pharmaceutical company who had encouraged a medical school classmate, who had become an emergency room physician on Long Island, to buy shares in her company because it was developing a promising drug. When confidential tests showed the drug did not work, the official tipped off her friend, who immediately sold his shares and relayed the tip to a patient who had also bought the stock. When the test results became public, the share price plunged. It appears that it was the patient who confessed what was going on and was rewarded for his cooperation with a reduced penalty.

That kind of investigation is unlikely to turn up a professional trader. Even if investigators find that a hedge fund made a large prescient trade, it might not stand out. After all, the fund made a lot of trades and can undoubtedly come up with explanations that do not involve inside information.

Back in the 1980s, Rudolph W. Giuliani, the United States attorney in Manhattan at the time, established his reputation by going after Wall Streeters. Those cases began with the normal procedure. The big break came when investigators noticed that a customer of a Swiss Bank branch in the Caribbean had made trades just before several takeover offers were announced. The customer, a high-ranking official at Drexel Burnham, an investment bank that financed a lot of hostile offers, had relied on Swiss bank secrecy laws to keep his identity confidential. When that did not work, he eventually named Ivan Boesky, a prominent speculator in takeover stocks, as someone to whom he had provided tips. A cascade of charges followed.

It seems unlikely that hedge fund traders are still talking about insider trading on the phone, now that they know the government may be listening. But even if they are, a ruling overturning the convictions of Mr. Newman and Mr. Chiasson could make it hard for prosecutors to ever win convictions. Traders will be careful never to discuss the actual payoffs to sources.

Call it the “plausible deniability” defense.

In trying to persuade the appellate judges to sustain the convictions, Antonia M. Apps, the prosecutor who won the convictions, referred at one point to the “sophistication” of the defendants. Judge Parker leapt on that, asking whether there was to be one rule for sophisticated traders and another for the unsophisticated.