Hello Neil,  some pianos have what's called a "study pedal" -- pushing
this pedal makes a rail come down with a strip of felt or cloth that
hangs between the strings and the hammers; in this way the sound of the
hammers hitting the strings is muted.  I assume it's easy to make some
sort of permanent or hand-operated rail inside the piano to make it
sound quiet.

http://commons.wikimedia.org/wiki/File:Cross-stringed_piano_Inside.jpg 

On the link above you find a picture with such a rail inside the piano.
The rail can move up and down by pressing the middle pedal.

Regards from the Netherlands,
Niels Berkers