NEW YORK–A statement last week by Tempur-Pedic’s president and CEO, Mark Sarvary, should jangle the nerves of those that manufacture bed pillows.

Speaking to financial analysts on a conference call about the company’s second-quarter results, Sarvary dropped this bomb: “Beyond mattresses, we’re excited about the potential for our pillow business.” He went on to say that Tempur-Pedic will launch a range of new pillows and a redesign of its existing pillow line at this week’s market.