By Dan Snierson
Updated June 11, 2009 at 05:53 AM EDT

The late-night wars are heating up: David Letterman’s The Late Show bested Conan O’Brien’s The Tonight Show in last night’s overnight ratings, 3.4/8 to 2.9/7, after only the seventh day of head-to-head competition. (The Leno-hosted Tonight Show consistently defeated The Late Show in the Nielsens.) O’Brien, who took over the reins of The Tonight Show on June 1, debuted with strong ratings but has seen numbers steadily dip since. These preliminary ratings do not reflect viewers’ demographic breakdown, and final numbers for O’Brien’s first week will be released on Thursday.