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?
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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!

@jroberson did you get an alert or is there an email in mailtrap?