Great news if you are interested in the background to the dozen or so treaties since 1958 where the original negotiations were via diplomatic conferences convoked by a resolution of the General Assembly. (If not sure please look at list below!) The UN Treaty website now includes free access access to the official records of those diplomatic conferences which negotiated drafts worked out by the International Law Commission and considered by the Sixth (Legal) Committee of the General Assembly. Not only is the reader promised access by individual document, but also searchable full-text versions of the entire collection of proceedings.
Law of the Sea, 1958
Conference on Elimination or Reduction of Future Statelessness, 1959-1961
Law of the Sea (Second Conference), 1960
Conference on Diplomatic Intercourse and Immunities, 1961
Conference on Consular Relations, 1963
Conference on the Law of Treaties, 1968-1969
Law of the Sea (Third Conference), 1973-1982
Conference on the Representation of States in their Relations with International Organizations, 1975
Conference on Succession of States in Respect of Treaties, 1977-1978
Conference on Succession of States in Respect of State Property, Archives and Debts, 1983
Conference on the Law of Treaties between States and International Organizations or between International Organizations, 1986
Conference on the Establishment of an International Criminal Court, 1998