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CBS’ “The Late Show with David Letterman” is carrying some ratings momentum into tonight’s finale, with Monday and Tuesday’s hours drawing some of the show’s best numbers in years.

Last night’s penultimate telecast, with guests Bill Murray and Bob Dylan, averaged a 4.9 household rating/12 share in Nielsen’s metered-market overnights — the show’s top rating since September 2009. It was up 48% from last Tuesday (3.3/9) and more than double the year-ago score (2.0/5).

And on Monday of this week, “Late Show with David Letterman” did a 4.1/11 in the overnights, a 37% improvement over last week (3.0/8), a 78% surge over last year (2.3/6).

On both nights, “Late Show” was No. 1 among latenight talkshows in the overnight household ratings, though NBC’s “Tonight Show Starring Jimmy Fallon” held a slight edge among adults 18-49 in the 25 markets with Local People Meters.

As expected, the final nights of Letterman on CBS have helped boost recent latenight addition James Corden. Tuesday’s broadcast of “The Late Late Show” averaged a 2.0/7 in the overnights — the best since Corden began as host in March and higher than any hour of the program, which had previously been hosted by Craig Ferguson, since February 2010 (2.1/7). It was up 33% from Tuesday of last week (1.5/5) and double what the program did with Ferguson a year ago (1.0/4).