The phrase optimal program specialization" was de ned by Jones et al. in 1993 to capture the idea of a specializer being strong enough to remove entire layers of interpretation. As it has become clear that it does not imply optimality" in the everyday meaning of the word, we propose to rename the concept Jones-optimality". We argue that the 1993 de nition of Jones-optimality is in principle impossible to ful l for strongly typed languages due to necessary encodings on the inputs and outputs of a well-typed self-interpreter. We propose a technical correction of the de nition which allows Jones-optimality to remain a meaningful concept for typed languages. We extend recent work by Hughes and by Taha and Makholm on the long-unsolved problem of Jones-optimal specialization for strongly typed languages. The methods of Taha and Makholm are enhanced to allow almost optimal" results when a self-interpreter is specialized to a typeincorrect program; how to do this has been a...