In recent years, heritage has become part of the venture-capital formula. Seems that the sight of a few venerable brands reinventing themselves has stimulated investors' appetites for other old names with glorious pasts. With the understandable optimism that comes with great wealth, they see themselves as Prince Charmings to the historic brands' Sleeping Beauties. Appoint a creative director, open a few flagship stores, develop some "icon" products, talk about "brand DNA" and—voilà!—the Sleeping Beauty has been transformed into a fully functioning retail princess, ready to be sold.

Burberry is perhaps the paradigm of a reinvented brand, and its Lazarus-like comeback is indeed a thing of wonder. Yet it has used its history very carefully. While looking into Burberry's past, I discovered that its eponymous founder was an anti-alcohol crusader; according to his 1926 obituary in the Daily News, "Mr. Burberry cared for little outside his business except temperance, religion and agriculture, and he never read novels." Apparently, he died at 91 after catching a chill while preaching at a Salvation Army meeting—hardly the model of fun-loving fashionista that today's Burberry would seem to appeal to.

What this suggests is that to thrive and prosper in the manner that Burberry has—reinventing itself as a cool, often edgy fashion brand—heritage must be used judiciously. Too much and you remain stuck in the past (temperance is not the great marketing tool it once was); too little and you might as well save yourself the bother of reviving an old brand and start a new one.

It was exactly this conundrum that sprang to mind when I bumped into the new owner of the luxury British jeweler Asprey, a charming man called John Rigas. Asprey was the first great Bond Street shop most people of my generation were familiar with. I have often kept a keen, sometimes critical, eye on developments there. And that is the problem for someone buying Asprey: thanks to the residual effect of all that heritage, people who have no part in the business and may not even have bought anything there for years feel they have a stake in the place because a long dead great-grandparent or distant great-aunt used to shop there.

Tongue firmly in cheek, I suggested to Rigas that as Asprey had been through a number of owners and a merger, then a de-merger, with Garrard, the best thing he could do was turn it into a shop where nothing cost more than a pound. Given the circumstances, he was commendably polite and told me that he was going to restore faith in a much-loved brand, which was good to hear. He was in the company of his creative director—a job, coincidentally, I was once offered long ago—a youngish man in a snappy suit, which tuned out to be Asprey-branded. It was nicely put together and, as I recall, had a flower loop on the back of the lapel—a touch that even some bespoke tailors omit these days. But should Asprey really be trying to break into the apparel market at all? Or would it be better off staying in its traditional areas of expertise: cocktail shakers, watches, jewelry and so on?

Selling garments can be a lucrative business, but should it be Asprey's business? On these occasions heritage can be a useful tool for divining what to do. Asprey did flirt with clothes between the two world wars, but the experiment was apparently unsuccessful. This is not to say that a heritage brand operating in one sector cannot move into another sector; Beretta, the gunmaker, has been family-owned since the Renaissance. It recently successfully moved into clothing, but its clothes are linked in performance, style or both to the world of guns—what the businessman would call Beretta's core competence.