Amplifier design parameters required for a good match for high (16+) ohm speakers?


Though I have a reasonable understanding of, or at least am satisfied with, the requirements for an amplifier asked to drive low impedance speakers, I am wondering about specific design parameters that might need be considered when mating an amplifier to high impedance ones. Asked another way: Are there specs that one should seek out when searching for an amplifier to be mated to such speakers?
mesch
Rodman, Thanks for the additional info!  I have taken a brief look at the additional links. I intend to peruse all the links provided again and possibly set up an upgrade project with my ST-70. Won't happen in the near future however, other things on to-do list. 

I don't remember the signal generator model. Built it fall of 1967. 

Thanks again, you have been most helpful!
Your welcome and I hope some of it’s useful(I try). btw: I found this power cable will fit the ST-70, with a rubber grommet and no need to further open the chassis’ original hole(after removing the strain relief, of course). I crossed and closed(without crushing) a couple cable ties around the cord inside, to prevent it’s escape(kinda Mickey Mouse). A snap to hard-wire, internally. It made an audible improvement, though I went cheap on that one(an experiment, at that point). No doubt, there are better cords now, just as small. https://www.zuaudio.com/classic-cables/birth-power-cable There’s an inexpensive/NOS one, currently on eBay: https://www.ebay.com/itm/Zu-Audio-Birth-power-cord-2m-6-5-ft-Brand-New-Factory-sealed/113672669785?h... Happy listening!
Ralph said it was in the best condition of amy he has seen for that time. It was factory manufactured, not put together as a kit. I own a original owners/instruction manual for the kit version so following it, I could likely replace the power supply caps myself if I feel the need.
If it came though here, then we replaced the filter caps. The ones installed allow the 5AR4 to be used, but do have a bit more capacity than stock. We also replaced the bias supply filter caps and rectifiers and probably the coupling capacitors too- the amp was set up to be reliable.
Ralph, I am using the 16ohm output with the Contrasts, which are rated at 16ohms. I am not sure about actual impedance within the bass frequencies.
Which model?
Ralph, I haven't put many hours on my ST-70 since I had you refurbish it in spring of 2016. However I now fell in position to do so. Took a long time for me to find a complimentary set of  speakers I could afford.  I have never any doubt that my ST-70 would prove reliable. As an aside, how do the St-70s fair when used in mono mode? 

Speakers are Contrast Model One AS3 Ref.