CBS’ “Late Show With David Letterman” beat NBC’s “The Tonight Show” for the first time in viewers for a full week of original broadcasts since December 2005.

“Late Show” delivered an average 3.46 million viewers for the week ending June 19 versus “The Tonight Show’s” 3.32 million, according to Nielsen live plus same day ratings.

“Late Show” garnered a 2.5 household rating for the week, once again beating “The Tonight Show” with 2.3.

The gap between the two late night programs among adults 18-49 is also narrowing. “Late Show” was just -0.5 rating points behind “The Tonight Show” this week, inching up from -0.6 last week and improving greatly from-1.4 during Conan’s premiere week.

–Vlada Gelman