I was wrong.

The moon isn't drifting away at the rate of a couple of centimeters a year - it's drifting away at around 4 cm/year.

As Space.com has it:

A billion years ago, the Moon was much closer to Earth than it will be tonight. Its tighter orbit meant it needed just 20 days to go around us, to make a lunar month. Other things were noticeably different, too. A day on Earth back then was only 18 hours long. People were probably wishing, "If only I had 24 hours in a day"

Okay, there were no people then, but the critters of the time eventually got their wish. In the intervening eons, the Moon has been drifting away. Each year, it moves about 1.6 inches (4 centimeters) farther into space.

[...]

During the past 4.5 billion years, Earth's overwhelming gravity has slowed the Moon's rotation down and pushed the satellite away. The cause is complex, involving tides, which we'll discuss below. One amazing result, for now, is a readily observable set of very interesting facts: It takes the Moon 29.5 days to make one revolution about its axis. All the while, of course, the Moon is also going around the Earth. This orbit also takes 29.5 days.

[...]

The high-tide bulges are pulled just ahead of an imaginary line connecting the centers of Earth and the Moon. It might seem rather amazing, but a terrestrial bulge of water has enough mass to tug at the Moon from yet another angle. The effect is to constantly prod the Moon into a higher orbit, which explains why it is moving away from us.

The Moon, meanwhile, is yanking back on the tidal bulges. So the water, down where it meets the ocean floor, rubs against Earth. This slows the planet down, explaining why there are 24 hours in a day instead of the mere 18 of a billion years ago.

[...]

Things continue to change, of course.

Earth's rotation rate is still slowing down -- our days are getting longer and longer. Eventually, our planet's tidal bulges will be assemble along that imaginary line running through the centers of both Earth and the Moon, and our planetary rotational change will pretty much cease. Earth's day will be a month long. When this happens, billions of years from now, the terrestrial month will be longer -- about 40 of our current days -- because during all this time the Moon will continue moving away.