From the text there are three things specified as being the "supreme Law of the Land"
1. This Constitution
2. the Laws of the United States
3. all Treaties made under the Authority of the United States
"This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land"
From the wording, it sounds like a treaty is not constrained by the Constitution, which seems a bit bizarre to me. Perhaps se need an Amendment to correct this.
At least treaties have to be ratified by Congress, not just signed by the President I think.
This is an old story.