What 's an overdamper?
In the overdamper the dampers are mounted above the hammers, instead of under. An obsolete system that is no longer used since 1910. Tuning takes half an hour longer than a regular piano, and the result is still disappointing. Also, breaking strings are common. Mostly the piano's look great, especially in a classical interior, but technically and musically they are the worst. Exceptions are the later overdampers by Blüthner and Ibach. The first picture below is a Blüthner from 1920.
Because of the extra tuning time I charge €90 on Wednesdays and €110 on Saturdays.
How to recognize the overdamper:
Open the lid at the top. If you see a wooden bar on top of the hammers (see photo with the text 'Lat') than you're in trouble, so to speak. If you remove the front panel, you can see vertical wires (draden in Dutch) in front of the action, hence the nickname "birdcage piano". The strings are almost invisible.
For an example of a modern piano (with visible strings) see this page.