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
Does your ST-70 still incorporate the 7199? If so- not much available, as far as tube rolling, now days. The EL34/6CA7 has never been known for a lot of dynamics, regarding bottom end. Sylvanias or Mullards, are what I had always kept in mine. They were much more plentiful(and- way less salty too), back then. No experience with what’s being manufactured now, so- can’t comment on their bottom-end performance. What rectifier are you using?  The Mullard(Blackburn plant)GZ34, is what I always recommend. Not that it offers any more juice, but- that it sounds so nice and lasts so long. I tried SS rectification(didn’t like it). You might contact Ralph and ask about beefing up your power supply(capacitance, etc), if that wasn’t already part of his refurb work. It’s been my experience, upgrading power supplies has always resulted in improved reproduction/greater dynamic impact, across the board.
I guess then, when considering an amplifiers rating into an 8ohm load, one should half that rating into a 16ohm load as a way of assessing that amplifiers ability to provide enough power for a particular circumstance.  
I always found that the ST-70 played better bass if it was possible to use the 16 ohm tap. This is assuming of course that the speaker was at least 16 ohms in the bass region!

The power rating of the amp actually goes up a watt or two as the output transformer is more efficient when used on a 16 ohm load.
Rodman, my ST-70 has the 5AR4 rectifier tube made by GE, and the 7199 driver tubes made by Conn in USA. Currently using JJ EL34 output tubes. I know the JJ EL34 could be replaced with a smoother tube. Any particular Mullards you might recommend?

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. 
If I still owned an ST-70, I’d be forced to purchase four of these(Did I mention, "salty"?): https://www.tubedepot.com/products/el34-mullard-double-o-getter-welded-plates I might be disposed to try the NOS, 1970s, Siemens version, toward the end of this page(and keeping a matched pair in each channel, if a matched quad couldn’t happen): http://www.audiotubes.com/el34.htm That page contains a lot of good info, if you’re going to shop EL34 types. How old are the Conns? Assuming you enjoy experimentation, here’s an easy/inexpensive way to enable you to try various NOS 6U8 type tubes(cheaper and more plentiful than the 7199), in your amp: https://tubedepot.com/products/6u8-to-7199-adapter Should you find a 6U8 tube, the sound of which pleases your tastes(Tung-Sol made some nice ones, in the 60s), it’s simple to move a couple leads on the tube sockets, obviating the adapter.   https://tubeworldexpress.com/collections/preamp/6u8a    Again- if the power supply capacitance is still stock(or aged), it’s still inadequate(by modern standards). Have fun and happy listening!
Rodman, Thanks very much for the additional info. 

Yes, I will likely shop for a different set of tubes and check out the Mullards offered by Tubedepot. I don't know when the Conn 7199 tubes were manufactured or how many hours are on them. I bought them when I received it back from Ralph.  If needing to replace them I would likely switch to the 6U8 tubes after removing the two leads. The power supply caps have been replaced, however I will have to call Ralph to see if capacitance has been increased. 

I believe my ST-70 was manufactured in 1969. The first numbers of the serial number is 69 and I know it came from that period. I was in storage for most of it's years and is in excellent condition. 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. I am not an electronics buff, however did build a single generator as a kit when in high school electronics class. Worked from the start. Kit was much as the ST-70 one, just follow directions step by step. Seems the craft is in making a good solder joint. 

Getting a little long winded today, am having fun!