I have Dynaudio Contour 1.3mkII speakers. They can tend towards the "bright" side or knock your socks off, all depending upon what you feed them. They knock my socks off mostly everytime these days, except perhaps with the very worst digital recordings, very few in fact.
I feed them:
Squeezebox TOuch->audioquest TOSLINK digital IC ->mhdt COnstantine SS DAC -> DNM Reson IC -> Audio Research sp16 tube pre-amp -> DNM Reson IC ->Bel CAnto ref1000m monoblocks-> Audioquest cv 6 wires -> Dynaudios.
ARC tube pre-amp is the biggest key to avoiding digital harshness I would say. A good tube pre-amp or tube buffer as Elizabeth suggests might be the most effective way to tame the harshness in OPs case as well I suspect.
A good tube pre-amp might be the ticket.
I also have the Dynaudios well apart jut a foot or two from sidewalls and with tweeters facing to the outside of my listening position, not firing direct. That alone (speaker placement/orientation) is an easy tweak to try without changing anything. This also tend to enable a bigger and more holographic soundstage in my small 12X12 listening room as well I find. The Dynaudios are great at that when set up accordingly.
The Dyns also tend to have just the right amount of dynamic attack and bite in the higher frequencies, very revealing but without being harsh or irritating this way. I love that about them! The Esotar tweeters Dynaudio uses are fantastic, but seem to require a bit of proper taming in set up it seems in order to be well behaved, especially with many digital recordings.