Phono Cart Impedance Question

I have a little bit of hiss through my 6 ohm, 0.28mV cart but only at a volume pushing the upper end of my listening volume...and it's only audible before I drop the needle, and even then not from the listening position.  I realize I therefore likely have a "non problem"!  

But I still have a generic question on to the sensitivity of producing hiss as it relates to cartridge impedance alone.  If one kept all other cart specs identical (including output of course) would you expect hiss to go up or down at the same volume and system gain if I used an 8 ohm or 12 ohm cart instead?  It seems like the hiss would likely go up just like moving to a higher impedance speaker under the same gain setup but perhaps I'm looking at this incorrectly? I realize moving to a slightly output cart could very well reduce the hiss.

Thoughts?   Sorry if this is a ridiculously obvious question and answer.

Back in the early 1980's, I had a preamp with three M/C cartridge impedance settings.  My neighbor, the factory sales rep, change one resistor to give me a 10 ohm setting.  It got rid of the hiss.
dan, possibly you got that result, because a 10-ohm load resistance would result in a very severe high frequency roll off in the audible range, using almost any cartridge except maybe a very LOMC with a 2-ohm or lower internal resistance.  You threw out the baby with the bathwater, as the saying goes.  "Hiss" is probably at about 2kHz or higher frequencies, usually.
In case anyone is curious, Keith confirmed what I was hearing was likely normal.  He indicated :

"There will be some white noise if you turn the level up beyond where you would normally listen as the VTPH-2A has a lot of gain and you would not want to play music at those levels.If you notice a significant difference between the two channels left and right then you may have a noisy tube (most likely a 12AX7)." 
Thx for the update.
Sort of confirms what a few were thinking.
Good luck and enjoy your music!