That's a good idea, thanks.
Will the cut tops root so I can end up with 3 more plants? If so, what would be the best way of rooting them?

I don't ever devide it. I do what Eldo says and then I root the cut off canes. Sometimes I stick them in a jar of water and sometimes I just stick them in a pot of soil and sometimes in the same pot as the ones I cut. They root very readily and you can end up with a lot more dracena plants than you want, which is a pretty nice complaint.

I agree with tache, except I would root them directly in a potting mix and skip the water. Take the cut-off canes and cut them off at the bottom until they are about a foot long. Plant them about 5 or 6 inches deep in a loose potting mix and keep the mix moist until you see new growth, which means they have rooted. You can then cut back on the water.

Thanks Eldo & Tache

Not having done this before makes me a bit hesitant to just cut off tops and leave a bare stem...Do I just make a straight cut and leave it like that? How long before they usually start new growth?

Is there any special care needed or just the normal common-sense stuff like keeping soil moist etc?

Apologies for what must be very basic questions for experienced persons but I am a relative newcomer to plants and my only experience is germinating seeds.

Another method of cane propagation (and the way it is often done commercially) is to take segments of your stem (cane) and insert them into your good potting medium LENGTHWISE, burying them about 2/3 of the way. Roots will emerge from the nodes and new shoots will develop at the 'eyes' on the nodes. Stem sections should include at least 2 nodes.

The attached illustation shows such a cutting, buried entirely underneath the soil (which you don't need to do).

The best time of year to do this is in the active growing season, when the days of the year are longer than the nights. Not only will you have a shrubbier 'mother plant', but several young plants to give away or grow yourself.

Here is a link that might be useful: {{gwi:51216}}

No pain, no gain. Just cut them short, because the new growth will begin near the top of the canes, and you don't want bare canes at the bottom.
The angle of the cut is not critical.
Don't keep it wet. Remember, there will be no leaves, so there won't be much moisture loss from transpiration.
Sometimes we have to take a leap of faith.
In Texas, we cut denuded nandinas clear to the ground in last winter/early spring. In a couple of months, beautiful, full "new" plants emerge from the root system.

Thanks to all

Great idea Rhizo