by "E flat" do you mean a half step down from standard EADGBe? this tuning is commonly known simply as "half step down" when you say E flat.... it can be interpreted as an open tuning to the E flat chord...

if so, when you release string tension from the neck you will notice some buzzing. heavier guage strings should help the matter or you may need to adjust the truss rod. try the heavier guage strings first and you shold notice a big difference.