Daryl Orbert has a brief look at how you can easily change the Deformer order in Maya. Like any other application, Maya has an evaluation order to things such as deformers. As an example, Maya will tend to, but not always evaluate things in the order that they were created.
A quick example of how to change your deformer evaluation in Maya
There are times when Maya applies a bit of intelligence. One example of that is if you have a bound skin on joints, along with blend shapes. Maya understands that the blends need to be evaluated before the skin cluster.
This might not be true when working with some other deformers such as the non linear deformers in Maya. This can be easily done by showing the inputs and outputs for a selected object in the scene, and then middle mouse click and dragging the order of the stack around.