The Nagata-Higman theorem states that an associative nil-algebra of bounded index n, without elements of additive order \(\leq n\), is nilpotent. An example due to \textit{G. V. Dorofeev} [Usp. Mat. Nauk 15, No.3(93), 147-150 (1960; Zbl 0095.023)] shows this theorem cannot be fully extended to Jordan algebras. However, the authors do prove that a special Jordan nil-algebra of bounded index n, without elements of additive order \(\leq 2n\), is solvable. They also prove that if J is a special Jordan algebra, A is an associative enveloping algebra for J, and I is a solvable ideal of J, then the ideal of A generated by the set \(I^ 2=\{frac{1}{2}(ab+ba) | a,b\in I\}\) is nilpotent.