But co-owners Denis Lefrancq and Martel Smith didn't make this change straight away.

They took over the restaurant in 2003 and right up till late 2006 it retained its formal atmosphere, that one-part-impressive-to-two-parts-intimidating feel that usually accompanies top-end dining. During that period, it enjoyed a word-of-mouth reputation that placed it safely among the top three restaurants in the city – deservedly so, I might add, as everything was top-notch. Sadly, this reputation did not result in a sufficient number of bums on seats, hence the move towards a more accessible brasserie style.

Much as it might have seemed like it, this was not the beginning of the end. Lefrancq and Smith did exactly what they said they would do: they stripped the restaurant of its austerity, pared down what was probably an excessively good wine list, and removed the slightly less necessary elements like the starched linen tablecloths, the pre-dinner amuse-bouche, and the hand-made petits fours.

All of this greatly reduced overheads, which they could then pass on in the form of lower, less exclusive prices. Crucially, what made this rather revolutionary change work is that they did it all without lowering the standard of what mattered most: the food.

Smith, once a promising young 20-something with Marco Pierre White among his referees, may not be a household name, but he is an established local chef in his own right, and he's been quietly producing bold modern European food with a heavy French
bias for years.

Looking at the options on the menu, and ignoring the lack of aforementioned table linen, you might be forgiven for not spotting a difference. But it is there. First and foremost in the prices, with some mains in the low teens, but also in the greater range of dishes available – further evidence of a restaurant that wants to broaden its appeal.

Lefrancq is on duty this evening – rather remarkably he seems to be permanently on duty – so the welcome we receive is smooth and efficient without being cold. When asked for advice on the wine selection, he's very helpful indeed, and his recommendation, a South African pinotage from Rhebokskloof Estate for £25, is exactly as full-flavoured and earthy as he said it would be.

While we wait for starters, we have a sneaky scan of the restaurant, and though the place has definitely had a makeover, it's hard to see where those cuts have been made. It's still a very smart space, with a beautiful dark wooden floor, quality upholstered banquette seat booths and a snazzy atrium-type skylight that floods the
place with light.

Yes, it's not as stuffy as it once was, but the only immediate change I can put my finger on is the lack of those tablecloths, and they can't have made that much difference to overheads surely?

I am grateful to be distracted from this conundrum by the arrival of dinner. A roast quail with apple, pine nuts and a cider vinaigrette (£8) is a solid effort, but is outshone by a risotto of ham hock, garden pea and mint (£6). Though it looked like the humbler of the two, the buttery texture of the rice and the deep savoury character of the salty ham put the decent but not so exciting quail in
its place.

The pinotage, which slightly overpowered the starters, comes into its own when paired with the mains – particularly with a fillet of beef, which proves a match made in heaven. Sadly, I can't say the same for the rest of the dish. Roast artichokes seem too tame and watery up against the bold flavour of the beef, and go a little too soggy in an over-abundance of red wine jus. That said, the fillet is as near to perfect as a piece of meat can get, and is almost worth the price of the dish (£18) on its own.

Confit of duck leg, with pomme cocotte, pear and cinnamon purée and a port wine sauce (£13) is good enough to notch up a victory, though again the accompaniments are not quite perfect, requiring a touch more salt, although reaching for the salt always feels like a terribly insulting thing to do if the chef is watching.

I consider creating some sort of distraction but settle for sneaking it to my wife under the table. If anyone notices, I can just claim I'm on a blind date. At least I win over dessert.

Poached peach sable with raspberry ripple (£5) is beautiful, and the ice cream a particularly nice touch, but there's just not that much of the peach amid the oh-so-pretty sable. My cheeseboard (£7) comes with plenty of it – half French, half English. (The French ones are
slightly better.)

Service throughout all this is swift, friendly, and virtually faultless, even if our other waiters do suffer a little in comparison to their boss, who finds the perfect balance between brasserie charm and upmarket finesse.

Those few niggles suggest Smith is perhaps no longer striving quite so hard to keep No 3 in that top three, but taking the whole package into account, it's still a very strong contender.

Given that you can now get three à la carte courses for just over £20, No 3 York Place remains a restaurant Leeds should be a little more proud of.

No 3 York Place, 3 York Place, Leeds, LS1 2DR, 0113 245 9922. Open Monday to Friday, noon-2pm and 7 till 10.30pm; Saturday 7 till 10.30pm. A la carte dinner for two with wine from about £28 a head.