Generating reproducible sequence of random numbers with SecureRandom [on hold]

I need to generate random numbers for an experiment (security is not an issue). I need my experiment to be reproducible, but I also need good randomness (something better than a linear congruential generator such as java.util.Random).

I've looked into SecureRandom, its generated numbers are not deterministic, even given a provided seed. Am I missing something? Is there a way to use SecureRandom in a way that yields reproducible sequence of random numbers?

Thanks!

Ofer