They are the ones who have managed to make a substantial profit, or avoid a swingeing loss, by buying or selling shares ahead of an announcement likely to have a big impact on their price.
Anyone buying shares in Anglia Television before MAI announced its takeover, for example, would have seen the value of their shares soar 37 per cent on the day the bid was launched.
Any bit of gossip - about redundancies at a friend's firm or a new order for a partner's company - could qualify as inside information if it concerns a company quoted on the Stock Exchange and the news has not been officially announced.
Hearing the information is not illegal, dealing in shares on the strength of it - or encouraging someone else to do so - is.
That does not stop it happening, however. In 1993, the Stock Exchange investigated 476 cases where there may have been a breach of its rules, and referred 79 of them to other regulators - principally the Department of Trade and Industry. That is likely to be just the tip of the iceberg because insider dealers have to be adept at covering their tracks by, for example, dealing through nominee accounts, buying or selling in small parcels or using a number of different stockbrokers.
The rewards can be high. One of the largest cases involved a circle of four high-flying City dealers, who passed information between themselves, making profits of between pounds 1,200 and pounds 20,000 a time. They were caught out when they dealt in Rank Hovis McDougall shares ahead of a takeover bid and were fined up to pounds 10,000 each in 1992.
One of the most celebrated offenders was Geoffrey Collier, former head of securities at the merchant bank Morgan Grenfell, who was fined pounds 25,000 and given a 12-month suspended sentence when he bought shares before a bid - but lost pounds 10,000 in the process.
Those five were relatively unlucky, however. Even if the Stock Exchange manages to penetrate the smokescreen, the chances of conviction are not high.
Of the seven people charged with insider dealing in four cases last year, none was convicted. The previous year was slightly more successful, with four convictions from the six charged. The maximum penalties for those found guilty are seven years in prison, and unlimited fines.
The rules were tightened significantly in March, when the Criminal Justice Act extended the definition of who is an insider and extended the prohibition on dealing to government and other gilt-edged stocks. But, while the City is alarmed by the implications of the changes, there is no guarantee it will make convictions easier to come by.
Initial investigations are done by the Stock Exchange's market supervision department but it has no power to prosecute, passing the information to the DTI instead.
If the President of the Board of Trade believes there has been a breach of the Act, he can appoint inspectors to investigate.
As in the Archer case, these will invariably be an accountant and a lawyer who have wide powers to question witnesses and examine documents relating to the case. They will then produce a report, but it is up to the trade and industry ministers to decide what action to take.