Hi Leslie -- first of all
!! Any Iris-lover is a friend of ours!
I don't know for sure what's going on with your rhizome specifically, but I can tell you that this sure was the winter for rot. And just like you described -- no smell to it, just mushy rhizomes. I think you've done what you can -- removing the rotted part and cleaning the remainder with bleach/water. If it were mine, I'd be inclined to leave the rhizome where it is and keep an eye on it. It's not likely that it will affect the other rhizomes, since this is not bacterial rot -- but rather *soggy soil* rot for lack of a better term. If anyone here thinks otherwise, I'll sure they'll chime in. I hope that you can salvage your Secret Rites -- it's a beauty!
