So how many free DVDs is a Richard Littlejohn worth to the sales figures?

How do you sell more newspapers in a declining market? There seem to be four ways: reduce its size; cut its price; give away a DVD - or hire Richard Littlejohn. The last is not proven, but we'll return to him later.

As the December circulation figures emerge - and this is a funny month what with Christmas and readers thinking of other things - there is frenzy in the market. Publishers are trying all kinds of approaches to the circulation problem, and some are trying more than one.

With the year just two weeks old, we have had an Observer re-launch, price cutting by the Express, a tide of DVDs... and Richard Littlejohn. Already fortunes have been spent on the columnist, and on TV advertising to back relaunches, DVDs and price cutting. There seems to be a bit of madness in the air, but then the newspaper business was never sensible.

Rupert Murdoch tells us he is now opposed to price cutting and giving away DVDs. But we don't entirely believe him, and anyway few are taking heed. The new year frenzy has DVDs still dominating the marketing, and they still work. This newspaper brings us one today, just as The Independent did yesterday.

The game has become more sophisticated and the need to choose the right DVD for the target audience more important. So the Independent titles select the sort of foreign movies their readers went to art houses to see when they were at university, while the Express offers the lesser-known classics of Cary Grant.

Linking Saturday with Sunday is increasingly important, making best use of cross-promotion and shared TV advertising.

With payments for rights and manufacture of the discs, DVDs cost around 30p a unit, which is a savage assault on margins. But the sales rewards can be huge. Conventional wisdom says the additional papers are bought for the DVD, and that these buyers are promiscuous and do not "stick". But the boosted circulation sticks in the monthly sales figures.

Everyone is looking for the bright idea. Last weekend, the Independent titles surprised even themselves with the success of a CD (on Saturday) and linked book (on Sunday), which added greatly to the sale of both issues. The subject was learning French in six weeks, on the face of it a dry subject for the detox period. On the contrary. Independent readers, and news-stand cruisers, were full of good intentions.

The national press spends to defend circulation and thus advertising revenues. Richard Desmond, owner of the Express and Star titles, is spending by deliberately cutting revenues. Knocking 10p off the price of the Daily Express - now 30p against the Daily Mail's 40p, and in both cases about 10p of that goes to the newsagent - is costing Desmond some £400,000 a week in reduced revenues. Early signs, over the first few days, suggest the sales gain is around 7 or 8 per cent. The sums don't work.

The fortress he seeks (hopelessly) to assault is the Daily Mail, the paper that understands Middle England, though it too is seeing its sales slipping. The paper chose to spend not on a price war but Littlejohn, Britain's first million-a-year journalist - a man whose profile and promotion are more akin to Wayne Rooney than the average hack.

In fact, the language of his reappearance in the Mail last week had something of the second coming about it. A third of the front page was given on several occasions to the pending and actual return of the "explosive column". "He's back" - in fact he had been writing for The Sun for the past four years.

Does Littlejohn sell copies like DVDs do? I doubt it. He has a way with vituperation, and is hatred of public sector workers, the politically correct and media studies, and his catchphrase "you couldn't make it up", may strike a chord with Mail readers. But somehow his second coming seems a little dated. Have readers moved on, perhaps, to the more cerebral rants of another Mail columnist, Melanie Phillips?

Can we, I wonder, devise an exchange rate for all these marketing strategies? Can we put a figure on how many DVDs a Littlejohn is worth? Can we put a figure on how much we would have to cut the price to gain the same sales lift as a DVD would provide? What would be the effect of reducing the size of a DVD? Would Littlejohn on a free DVD gain more sales than Littlejohn on a page? I am working on it, but it is not a pure science.

But what about the audited, real (well, fairly real), figures? Comparing December with the previous month means little. Better to compare the figures with the same month a year ago, or to look at the figures averaged over a six-month period compared with the same period a year ago.

The year-on-year figures tell us The Times is up a bit, The Daily Telegraph and Independent down a bit, and The Guardian up significantly (it is still gaining from the Berliner relaunch three months ago). In the mid market, the Mail and Express are down - the latter hugely so, though much of this is due to removing bulk discounted sales. The red-top tabloids are all down.

The Sunday story is not dissimilar. This time it is The Independent on Sunday with the highest increase in sales, 7.2 per cent. Only one other Sunday paper boosted sales year-on-year, and that was The Sunday Times, up 0.64 per cent. Having followed its pioneering sister daily along the downsizing route, the IoS is reaping the benefits - further proof that reducing the size wins readers.

Will The Observer relaunch achieve the same? One issue, accompanied by expensive TV advertising and the sampling that novelty inevitably brings about, tells us little, although the editor will have been happy to put on the extra 80,000 copies industry estimates suggest. Give it a few weeks to draw serious conclusions, but no quality national newspaper downsizing has yet failed to lift sales.

Simply relaunching in the old format does not have the same effect. The Sunday Telegraph, under its new editor Sarah Sands, was revamped last autumn to make it more cuddly. Its year-on-year sale is down 6.6 per cent. With The Daily Telegraph recording its first sub- 900,000 sale for more than 20 years, the quiet revolution going on in that group clearly has further to go.

Peter Cole is professor of journalism at the University of Sheffield