Sure. Personally, I think the use of polyphonic settings is a bit too much for a simple office like compline, but depending on the occasion it might work.

The Kyrie isn't sung at compline. After the "Misereatur nostri" or "May almighty God" the hymn is sung straight away.
For the hymn, alternating between Gregorian chant and a polyphonic setting by Thomas Tallis (or this one, also by Tallis) could be beautiful.

See my booklet Ad Completorium for the Gregorian chants of compline.

The Royal School of Church Music, King's College Course does a fully sung compline (all chant and polyphony) every night of the week-long course. RSCM is an Anglican program, of course, but I think the Order of Worship for Compline is the same, or at least very nearly the same, as the Roman office.

Their website is here:
http://www.kingscollegecourse.com/

You can poke around to find recordings and also contact details to find out more info on what settings they use.

I think the Order of Worship for Compline is the same, or at least very nearly the same, as the Roman office

Definitely not the same... I guess we'd have to define "very nearly the same," but not really. You can tell that they're cousins, but the elements are quite differently ordered.

What utter liturgical sanity!
What pure intellect of worship!

What utter liturgical sanity!

I realized recently that my personal bar for quality liturgy has gotten pretty low.
All I want, these days, is to be able to go to church and NOT continuously think to myself, "This is totally insane. Why are they doing that?"

I recently went to daily Mass for no reason other than that I was seriously hoping there wouldn't be any music. Alas, there was.

No, that was the Schola Cantorum Franciscana in 2013 singing in Pittsburgh. This is Louisville:
https://www.youtube.com/watch?v=9rAkOW_XM2k&list=UUE6GW_dd8Fb9U_RRxzyDyJQ

I used to run an annual early music festival in Winchester, UK and our biggest attendance each year (400+) was entirely in Latin, "Sung Compline from the time of Palestrina" in the enormous Winchester Cathedral, by candlelight. With 6 professional male singers, amidst much chant, we sang, polyphonically, Compline hymns such as "In manus" and "Te lucis", Nunc Dimittis (with antiphon), as well as the prescribed Marian antiphon at the end. Composers included Palestrina, Victoria, Whyte, Byrd, Tallis and Sheppard. While mainly a festival of music concerts, this particular event was free and open to the public, and we found that Catholics from all over the south of England were making a special trip for this each year. People are hungry.

Richard and ModTrad,
It's good to hear other views about Compline doins'. The Compline Choir in Seattle does Compline every Sunday night at 9:30 p.m. Pacific Standard time, except if it falls on Christmas. You can listen to their live broadcast by opening KING FM Seattle on your computer and following the prompts. We seldom miss listening to this group. Of course if you live in a far off time zone, you takes your chances with the schedule. Last May, my son and I made the pilgrimage to Seattle for a Festive Memorial for Peter Hallock. We drove our truck camper north and stayed in the church parking lot. It was a festival of his music and more. At a tribute supper, Matt and I were invited to sing with the Compline Choir on that Sunday Evening, about an hour hence. Wow, those guys are good. There were 32 men chanting Compline that Sunday night what with all the returnees. I was standing next to a very old guy in the second alto section (who looked like he could have been in the band in the 1950's), back for the Memorial Compline, during the short rehearsal, and he turned and looked at me and said, "I don't remember seeing you here before." I said, " Oh, I've never sung with this group before, I just came in off the street." In conversing with Peter Hallock, he stressed the importance of making the Office of Compline into your own template. That way, you will own it. He discussed the importance of certain parts of Compline as they morphed over the centuries and put the immutable singing of the Psalms as ground zero. He said in the Order for Compline all else may fall away except for the Psalm. In his own work, he also pumped the mystical. For me, the apex of Compline is in the singing of, "In manus tuas, Domine, commendo spiritum meum", which is the last thing said by a dying person in the Roman tradition, which brings me to what I call the Compline interface. The window into your own death is Compline: the last 25 minutes before you meet your maker: going into that dark night; your soul laid bare. When I started our first group the most difficult music to find were Psalm settings. So using Peter Hallock's style I started making my own settings, along with realizations of Roman and Harmonized Anglican Chant Psalms. I now have about 250 Psalm settings of all stripes, not counting the 45 of Peter Hallock. Plainsong. two part harmonized. 4 part harmonized. More than half of our members are instrumentalists, (aka: notation means something) so it geared to them. I now have about 100 pieces that call themselves, Nunc dimittis. The most important thing for me was to make the arrangements very accessible to the singers in terms of notation. You never have enough rehearsal time, and we've gotten a couple of our groups down to one rehearsal for Compline. For a year, we prayed Compline every fortnight, and one June had Compline all 5 Sundays. Even with 4 groups, it was too much for them so we bailed back to once a month; alternating.
Thanks for reading.
jefe, bass trombonist; 22,000 services with the LAPhil, 1969-2006.