AnalogRead too slow... Faster alternative? For a program that I'm working on, I want to get an accurate reading from a noisy pressure sensor.  So, the idea that I have is to do a thousand AnalogRead commands on the same port very quickly and then average them.  The pressure readings become very precise, however, the program that I am running becomes very slow.  I need my program to be orders of magnitude faster.

I'm sure that there's a faster way to do AnalogRead commands, especially because I am requesting the same port over and over.  Maybe there's a way that I can take lower resolutions of readings and then average those?  I don't know.  Can anyone help me?  I am an amateur Arduino user looking to learn.  

I have done a little bit of research on my own and had trouble finding concrete examples.
Ignacio's proposal is surely a good one if you really need higher sample rates, but I would try another approach: 
Average your signal before sampling it! This can be done by connecting a simple RC lowpass to your AD input. 
With that you get rid off those high frequency noise you don't need, but without wasting CPU time.