Positioning, the 2008 Formula One world champion told British reporters gathered round him in the Mercedes harbourside motorhome, is everything in Monaco.
The Briton was referring to the special skills required to win the most glamorous and glittering race on the calendar but Roscoe demonstrated that positioning was important in other ways as well.
Nestled with his head on Hamilton's lap, the puppy stretched out comfortably on the bench alongside and started to snore - loudly.
"He was out late last night," said Hamilton, smiling as he completely lost the thread of the conversation amid general laughter.
"He does it all the time. When I go to bed, he sits next to the bed or on it, and that's how he snores."
Hamilton - who has a colourful new helmet for Monaco with a cartoon of himself, Roscoe and American pop singer girlfriend Nicole Scherzinger together in a car - could also be sitting pretty this weekend if Mercedes can repeat their qualifying form of the past three races.
The team are chasing their fourth pole position in a row, with Hamilton's German team mate Nico Rosberg looking for a hat-trick.
In Spain earlier this month, the pair swept the front row but struggled with the tyres in the race. Hamilton went from second to 12th and was lapped but Monaco is kinder on the tyres and far harder for drivers to overtake.
"Positioning is everything here and if we can get on the front row then that will put us in good stead for the race," said Hamilton.
"In 2007 I was in second and I couldn't get past Fernando (Alonso). Last year no-one could get past (Mark) Webber, it was just a train, so you can create a train here.
"The best chance is when you get on pole position. (Spain) was my best chance to get a win and we didn't do it. This is another chance, another opportunity to do that."
Mercedes were mystified after Barcelona about why their tyres lost performance so quickly, with the team looking at everything from procedures to how the drivers handled the tyres. Hamilton was optimistic that progress had been made.
"There has been a huge reaction from the guys to the result. Everyone is working as hard as they can to improve and understand the tyres," he said.
"We still need to experiment, to try different pressures, different temperatures and all those kind of things. We just find the right path ourselves and hopefully we will find that sooner rather than later."
Hamilton has had two third places in five races, already much better than many had predicted when he left McLaren at the end of last season for a team struggling to be competitive.
However, such had been Mercedes' improvement that it came as a real shock to struggle so much in the first race back in Europe after the long haul rounds in Asia and the Middle East.
"We were on a bit of a high," he said. "To see us then go back that far was definitely a huge surprise and put us on the back foot a little...but I feel positive about this weekend, I'm re-energised, refocused and ready for another challenge.
"Spain could easily be repeated if we get it wrong, although I don't think it's going to happen because we have learned, and we are learning and improving. We went a direction in the last race with the car and tyres that didn't help.
"The problems we had in the previous races weren't too big, so we have taken a step back and gone in a different direction."
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