How can I make the volume change in smaller increments?

When I press the volume up/down keys on my keyboard, the volume changes too much. How can I make the step size smaller so that I have finer control?

Ubuntu 17.10 and later

It's worth noting that on Ubuntu 17.10 and later with GNOME Shell, there is already (albeit somewhat convoluted) kind of support for this.

Press Shift+XF86AudioRaiseVolume or Shift+XF86AudioLowerVolume (usually the dedicated volume up / down keys on the keyboard) to change the volume with a smaller step size.

Ubuntu 14.04 / 15.04 / 15.10 / 16.04 / 16.10 / 17.04

I finally have a proper solution for Trusty, Vivid, Wily, Xenial, Yakkety, and Zesty users. Rather than using a bunch of hacks or a script, I decided to fix the problem in the source code. I applied this patch (now broken) to gnome-settings-daemon and unity-settings-daemon (some trivial modifications were made to the patch).

I have uploaded the packages to a PPA:

ppa:george-edison55/gnome-settings-daemon (Click here for instructions on using PPAs.)

Once you've added the PPA, run:

sudo apt-get update
sudo apt-get upgrade

You will need to restart after installation completes. Once the packages have been upgraded, you can use the dconf command to change the volume increment:

dconf write /org/gnome/settings-daemon/plugins/sound/volume-step 2

(The default value is 6.)

Now when you press the volume keys, the volume will change in increments of 2: