Freshman medical drama Three Rivers and veteran Cold Case have been struggling since the start of the season. Last night, there was an increase in viewership. So, does that mean that they’re safe?

Three Rivers revolves around a group of physicians and their support staff who help needy patients get life-saving organ transplants. The series stars Alex O’Loughlin, Katherine Moennig, Daniel Henney, Justina Machado, Christopher Hanke, Amber Clayton, and Alfre Woodard.

Cold Case follows a team of Philadelphia police detectives who work to solve long-unsolved murders. The venerable drama features Kathryn Morris, Danny Pino, John Finn, Jeremy Ratchford, Thom Barry, and Tracie Thoms.

As many fans of these shows are well aware, the series have been struggling in the ratings.

The first six installments of Three Rivers averaged a poor 1.8 in the 18-49 demographic and 7.93 million total viewers. Last night, the numbers bumped up a bit to a 2.0 rating and 8.45 million viewers. While that’s an increase of 10%, the numbers are still not good. The series is unlikely to be saved from cancellation but word is that the network is considering ordering up to five additional installments.

The situation is similar for Cold Case. While the veteran crime drama will still likely air a full season of 22 episodes, it’s very unlikely to return for 2010-11.

Likely because they have nothing to lose, CBS execs are changing up the schedule a bit for next week, says THR. Cold Case will air at 9pm and Three Rivers will get the 10pm slot.

In the past, Cold Case has performed well with a strong lead-in and this change will give it a better lead-in with The Amazing Race. The 10pm timeslot is a bit less competitive so that might help Three Rivers. Or conversely, the move might confuse viewers and both shows could sink lower in the ratings.

What do you think? Is this a good move for Three Rivers and Cold Case or more like “rearranging the deck chairs on the Titantic?”

Images courtesy CBS.