It happened to me already couple of times: in shooting mode A can't get underexposed pictures using exposure compensation dial. Just in case I found a pretty big table with restrictions on camera settings on the back of manual. There is no particular mention about any restrictions on exposure compensation, why would be anyway it wouldn't simply make sense... unless I am not aware of something. I shoot with 7D, and I am new to Fujifilm world. Any idea what is going on?
You're probably running into the shutter speed restriction that limits how fast you can make it in Aperture Priority mode, because it's limited by the selected aperture. On a sunny day if the aperture is too wide you might see the shutter speed turn red in the LCD display, indicating that the shutter speed won't go any faster. This limit depends on a lot of factors, including not only the aperture selected, but also the focal length you're using. The DR and resolution (L vs M) may also have an effect. At the widest aperture you might see 1/1000th sec. appear red, and if you try to give it some negative EC, nothing happens because the X10 won't allow a faster shutter speed. As you close the aperture you'll change the shutter speed limit, which will now allow 1/1200, 1/1500, 1/2000, etc.
Don't ask me
why Fuji does this, because it has
lots of interdependencies. For instance, with most of its EXR cameras (I haven't specifically checked this with the X10) when you're shooting at night and it's really dark, you'd think that with the camera on a tripod you could use a really slow shutter speed and a high ISO to get a good exposure. But in really low light, Fuji links the shutter speed with the ISO level, so if you raise the ISO by one stop, the slowest allowed shutter speed changes by the same amount, so the exposure doesn't change. The Canon P&S cameras that I've tried don't do this, and the Nikon P&S cameras are somewhere in between.