If you may have owned your house for a long time, then your assessed values probably have increased sharply. However, your taxable values have increased slowly, because the increases are capped. As a consequence, you may see on your "Notice" that your taxable value is far less than your assessed value.
Even if you appeal and get your assessed value reduced, it still is likely to be higher than your taxable value. If your taxable value is not lower, your taxes will not go down.
Indeed, your taxes may go up anyhow! Even if your assessed value has fallen during 2008-10, it still may be far above your taxable value. If so, your taxable value can continue to go up by the amount allowed by Proposition A. And as the taxable value is higher, so is your tax.
Bottom line: your tax goes up even as your assessed value goes down!
This has happened to many long time residents. Keep remembering, however, that even though your tax went up, the cap on your taxable value still is holding your tax below what it otherwise would be.
If your assessed value is twice your taxable value, then without the Proposition A cap, your tax would be twice as high as it is now!
If your taxable value is capped far below your assessed value, then you are not likely to reduce your property tax bill by appealing your assessed value.