A few weeks into the Chris Licht era as showrunner of “The Late Show with Stephen Colbert,” the CBS program has shown some positive ratings signs.

NBC’s “The Tonight Show Starring Jimmy Fallon” is in no immediate danger of losing its status as the top-rated late-night program, but the Eye’s 11:35 p.m. entry has strung together three straight second-place demo finishes for the first time this year. And last week, with guests including Bill O’Reilly, Rob Reiner and Judge Judy Sheindlin, “Late Show” posted its most competitive demo finish relative to Fallon originals since last October while also drawing its largest weekly audience in nearly three months.

According to Nielsen estimates for the May 2-6 frame, “Late Show” averaged a 0.51 rating in adults 18-49 — his top score for a full week since mid-February — to pull within three tenths of Fallon (0.81) while beating ABC’s “Jimmy Kimmel Live” (0.45) by 0.06. Colbert and Kimmel have been in a tight battle most weeks for second in 18-49, and last week’s 13% advantage represented the CBS host’s biggest lead over original “Kimmel” episodes since January.

In total viewers, “Tonight Show” led comfortably with 3.204 million, followed by “Late Show” at 2.573 million and “Kimmel” at 2.122 million. This was the largest audience for “Late Show” since Feb. 15-19 (2.744 million) and its largest lead over the ABC show (452,000) since that same frame.

CBS last month tapped Licht, a former CBS News vice president who has been executive producer of the network’s rising “CBS This Morning,” as showrunner of “The Late Show with Stephen Colbert.” The network knows it will take time to alter the late-night ratings landscape, but is hoping some changes, including a tighter opening and a greater emphasis on newsmaker interviews can make “Late Show” more relevant in the months leading up to the presidential election.

Also showing some improvement is “The Late, Late Show with James Corden,” which has made some noise with its popular Carpool Karaoke segments. For the week of May 2-6, “Late, Late Show” was up a smidge from the previous week to earn its highest 18-49 average (0.32) since the week following its post-Super Bowl special.

NBC’s “Late Night With Seth Meyers” remained on top (0.41, a four-week high), but its margin of victory this spring has narrowed. In total viewers, Meyers led with 1.458 million viewers to 1.271 million for Corden. ABC’s “Nightline” averaged 1.426 million viewers (and a 0.30 in 18-49) for its half-hour post-Kimmel.