How to create a repeatable incompressible fast InputStream in Java?

For HTTP performance testing, I'm searching for a way to generate data as efficiently as possible for a repeatable Java InputStream which is incompressible by HTTP gzip compression (or as close as possible). I found this blog post on Randomly Generated Input Stream which already does a very good job of providing a fast random number generator for an input stream and which is nearly incompressible, but it is not repeatable.

The requirements are:

• use minimal CPU resources
• be repeatable (e.g. always return the same results when read from beginning)
• produce an output stream which is as incompressible as possible
• produce output as fast as possible (e.g. not limited by disk I/O)

I'd be glad to get some tips or pointers how these requirements could be met.