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
If you can solder and read simple schematics, improving the ST-70 is cake. There’s a wealth of info available. Just restrict yourself to those best reviewed, far as advice(ie: Ralph). Joe Curcio gave me some valuable tips, on how to increase my Joules, without adding/changing anything outside the chassis.  Regarding that wire swap, you might want to save this: http://lib.store.yahoo.net/lib/thetubestore/6U8A-7199.pdf Don’t know if Joe still offers free advice, but: http://www.curcioaudio.com/dynadr_3.htm#DYNACO%20STEREO%2070%20POWER%20AMPLIFIER           Was that a Heathkit Mod #IG 5282, in a blue plastic case? Wasn’t my first build, but it wound up working for years, testing speaker drivers in my shoppe.
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?