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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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?

what about user @mesch