Alternatively, instead of feeling that one is bound to make sure some form of dominant is included, a different approach to accompaniment can be taken.

It is true that a dominant chord in conventional harmony serves to establish the tonality of a piece, but the mood and feel of ones music can be given a different quality through the use of non standard chord combinations.

I played for years with a goosd ear and a good instinct for music, and have never found it hard to fit good chords to music, modal or otherwise, and I had no idea what perfect cadence was, much less functional harmony.

In modal music, as long as the strong notes in the melody are notes 1, 3, 5 and 7, with the others being used more as passing notes, and as long as note 1 is referred to throughout, I think you could, for the sake of tension, get away with playing any combination of 2 or 3 chrds from the chords of the mixolydian and it would sound ok.

I can imagine singing a tune in D Dorian with just the chord of C major to accompany me and it sounding good and clearly having a sense of D tonality as long as the tune explicitly implies D as the tonality, again with lots of emphasis on notes 1,3 and 5, but also note 7 with repeated referecct to note 1.

Make sense?