The designers were set a brief to create a stacking wooden stool with a distinctive aesthetic, which the Newcastle upon Tyne-based brand had identified as an underserved niche in the contract furniture market.
"Timber stools exude quality and durability, but often at the expense of reduced utility and high transport costs due to their method of assembly," Deadgood's design director, Vicki Leach told Dezeen.
"The Lap Stool bridges that gap and offers commercial projects much more flexibility and functionality, whilst not having to make concessions on using this high-quality, tactile material."
Deadgood approached SmithMatthias for the project because of their reputation for creating straightforward, functional products that celebrate the materials and processes used in their manufacture.
The designers began by sketching out a basic form that they developed through a process of hands-on model making. This eventually culminated in a decision to focus on the lap joint as a key detail in the design.
"Our usual process is to sketch together and get in the workshop to develop ideas," explained Matthias.
"The leg assembly was born through sketching but it wasn't until we started playing around in the workshop that the leg joint was decided."
Two angled pieces of wood meet at the top to form the stool's A-shaped frame. Some of the material is cut away from each piece to create the distinctive overlapping joint that the stool was named after.
"The lap joint is a time-honoured method of securely joining pieces of overlapping timber," Leach added.
"The way in which the leg is designed offers supreme strength, whilst at the same time revealing an intriguing and honest detail that tells the story of the craft."
The product is made from solid European oak with a natural or black lacquered finish. The user sits on a simple seat with rounded edges, while a bent-metal footrest enhances the sitter's comfort.
According to Smith, the stool is best suited to use in contexts such as bars, restaurants and workplaces requiring furniture that is versatile and easy to move around.
The Lap Stool was launched at an event at Deadgood's showroom in London's Clerkenwell on 20 November. The product is available for pre-order, with the first stock shipping in January 2020.
Deadgood was co-founded in 2005 by Dan Ziglam and Elliot Brook, who set out to build a portfolio of characterful furniture, lighting and interior products that are made in Britain.
The company has worked with many emerging designers over the years, including Daniel Schofield, who designed a leather lampshade with a laser-cut pattern inspired by brogue shoes; Max Lamb, who created an anodised aluminium table; and David Irwin, whose pentagonal pendant lights for the brand are held together by silicon bands.