Depends on your definition of "unwanted". Tube amps distort. Even when played lightly. When you are "in the room" the sheer volume causes your ears to compress which masks much of this. People are often shocked as to how distorted their amp sounds when mic'd up in isolation.
In the 70's CBS attempted to rid Fender amps of this "unwanted distortion" and ushered in the era of sterile, squeaky-clean amps which ultimately led to disco music and we all know how that turned out. Fortunately the next owners were wise enough to undo these "improvements".
So, assuming it's natural tube amp distortion the first solution is to always turn down the gain and/or MV. It will feel sterile and lifeless because that's what happens when you turn down the gain. Add a compressor before or after the amp block to give some compression.
Now it could be some other distortion but without clips it's just speculation.
