Food trading director Darren Blackhurst said that as part of its work to restore its position as the market's price leader, Asda was ditching any activity that it felt was designed to hide the true price of a product.
He added: "What's important to us and our customers is low prices. We do not want our business to hide behind the high price jargon that we sometimes see in the industry."
Blackhurst highlighted Mars ice cream sold for years at £1.99 a pack, usually on bogof. "The price in Asda is £1 for a pack. You can't run a bogof on that but £1 is the right price for that product." But the retailer would continue to run promotions, stressed Blackhurst. "Consumers like low prices and great offers and we will deliver both - but not through gimmicks. Lines will be sold at 'one for a price' or 'two for a price'. We will make it simple."
Asda is now running hundreds of 'two-fors' in store. And Blackhurst said these were driving "really big" volume uplifts.
He added: "Mums tell us that when they find bogofs it's always on fringe products that they don't really need. But when we do 'two-fors' they are on core products so they are saving where they need to save and on things they want to buy two of."
While the switch out of popular bogofs and into 'two-fors' is definitely on-message for the EDLP retailer, rivals are sceptical.
One trading director said: "What they are doing is impactful but whether it will be as strong as a bogof only time will tell. They may also not get the same supplier recovery - particularly on big brands, which always want something in return for their funds."
Asda has also been breathing new life into its Rollback programme. Blackhurst said: "Shoppers know they can trust us to have permanently low prices. We have rolled back 2,000 prices since the start of the year and that's really kicking in now."
He denied Rollback was being used for temporary price cuts. "We will not allow it to be bastardised. It's about a permanent price position so that our customers can trust us every time they come in."
Research from Assosia, the company that supplies The Grocer with data for its Promotrack section, shows that Asda has cut its bogof promotions in favour of multi-buy and save mechanics. This week, 45% of Asda's promotions came under the banner of 'save'.
There is nothing new in Asda's approach to pricing and promotions. Allan Leighton adopted a similar approach in the 1990s.
But this time around Asda's focus on EDLP has been accompanied by efforts to improve buying terms, which have caused protests from suppliers.
l?Asda parent Wal-Mart said this week that first-quarter profits at its UK operation fell "slightly" as Tesco pulled further ahead.The UK market continued to be "soft", said Mike Duke, vice president of Wal-Mart International, adding: "We're focused on attracting more selective shoppers."
Duke added that Asda, whose second Essentials store opened in Pontefract this week, was planning to open 25-30 new stores in the course of this year.