A fly is trapped in a bottle which in turn is in a bucket of water.

In order to fly upwards, the fly must exert a downward force greater
than its own weight on the bottle, this force initially being applied
directly when it takes off, and subsequently passed through the
intervening air when it is airborne.  Thus, when the fly is flying
upwards, the bottle will certainly stay put on the floor of the bucket.

If the fly then chooses to fly downwards, it is then exerting a
downward force _less_ than its own weight on the bottle, and perhaps
even an upward force if it actively beats its wings to descend rather
than just letting itself drop.  Thus, depending on the overall density
of the bottle (including the air and the fly contained within it) and
any extra forces imparted by the fly, the bottle may begin to rise when
the fly is travelling downwards.  The bottle will certainly begin to
sink again if the fly lands anywhere on it, hovers in the air, or
starts flying upwards.

To make this puzzle clearer, it might be helpful to state that the
weight of the fly at rest is _just_ enough to cause the bottle to sink.
Is that what you meant above by "the bottle just sinks"?

-- Mathew Hendry <m.hendry@dial.pipex.com>

[ Editor: the same posting also answered the monkey-and-pulley puzzle,
which is physics/monkey. ]