Stephen
String pressure on the saddle is very important (especially for an under-saddle pickup to function properly), and can only be achieved if the saddle stands up well clear of the top of the bridge like this.
Not like this
By the sound of it your guitar might need a neck re-set - usually only found in older instruments and caused by years of pulling pressure from the strings.
You can check the neck-set (pitch) of your guitar by putting a straight edge on top of the frets and slide it towards the bridge. If it meets well below the edge of the bridge like in this photograph, the guitar will most probably need a re-set.
This one is way too low
The neck angle is changed relatively so that the head stock position is moved back towards the player in relation to the way it is currently. That will allow for the action to be lowered and at the same time to install a taller saddle in the bridge.
The process to check the neck angle (pitch) is explained here:
http://www.frets.com/FretsPages/Musician/Guitar/Setup/NeckAngle/neckangle.html
And the re-set of the neck here:
http://www.frets.com/FretsPages/Luthier/Technique/Guitar/NeckReset/00028Reset/00028reset01.html
You can sandwich veneer of any hardwood in-between the existing saddle and the root of the saddle slot in the bridge (below the pick-up) or you can just replace the saddle with a new (higher) one has the same effect, but as you might have gathered, both actions will raise the position of the strings above the fret board and making the guitar less playable.
