first tube rolling: expert advice needed - take 2

Annoyingly my first thread that went under this header has disappeared. Apologies to everyone who had contributed and put a lot of thinking into this.

Here is the plot again: I had bought a second hand Unison Research Unico SE hybrid integrated amp with two Electro Harmonix 12AU7A in the pre-amp section. Very fine in musical terms, the amp caused an unacceptable (in my solid-state biassed opinion) amount of hiss and slight traces of hum coming from the speakers in silent parts. I had assumed this was caused by (perhaps defective) tubes. Not knowing where or what substitutes to start searching for, I have had the benefit of Audiogoner's advice and finally acquired a pair of NOS tubes at Machmat in the Netherlands, namely:
Tesla ECC802S unused NOS (virtually the same as Telefunken's ECC802S, I have been told, picture: see my "Guests" system).

Here is the good news: Am I glad I tried this! I am getting a cleaner and more saturated sound, as if creases had been ironed out; bass appears more finely detailed (tried this with different speakers with reproducible results)
And here is the bad news: The hiss is still there, perhaps even more disturbing than before because the music is better. Guess I'll have to have the amp inspected and probed (hope I haven't been "had"). Anyway, if it doesn't work out with this machine, I'll be looking at a full valve integrated from Unison (I do like this sound).

One tip I gladly pass on (not just to the Europeans): Mattijs de Vries of Machmat sure is someone to rely on!
http://www.machmat.com/index.htm

Finally one question to the experts: Is there something like a burn-in procedure I should observe or time I must allow for with unused NOS?

Thanks in advance and regards
Karel