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A \((v,k,t)\) trade \(T = T_1 – T_2\) of volume \(m\) consists of two disjoint collections \(T_1\) and \(T_2\), each containing \(m\) blocks (\(k\)-subsets) such that every \(t\)-subset is contained in the same number of blocks in \(T_1\) and \(T_2\). If each \(t\)-subset occurs at most once in \(T_1\), then \(T\) is called a Steiner \((k,t)\) trade. In this paper, the spectrum (that is, the set of allowable volumes) of Steiner trades is discussed, with particular reference to the case \(t = 2\). It is shown that the volume of a Steiner \((k, 2)\) trade is at least \(2k – 2\) and cannot equal \(2k – 1\). We show how to construct a Steiner \((k, 2)\) trade of volume \(m\) when \(m \geq 3k – 3\), or \(m\) is even and \(2k – 2 \leq m \leq 3k – 4\). For \(k = 5\) or \(6\), the non-existence of Steiner \((k,2)\) trades of volume \(2k + 1\) is demonstrated, and for \(k = 7\), we exhibit a Steiner \((k,2)\) trade of volume \(2k + 1\). In addition, the structure of Steiner \((k,2)\) trades of volumes \(2k – 2\) and \(2k\) (\(k \neq 3,4\)) is shown to be unique. A generalisation of our constructions to trades with blocks based on arbitrary simple graphs is also presented.