Two generalizations of shininess

Shininess is one of the main theory combination methods in Satisfiability Modulo Theories. We present two infinite families of generalizations of it: one involving a property between gentleness and shininess, which helps us see gentleness itself as a variation of shininess; and another having no further computability requirements on the weaker theory, in addition dropping the need for smoothness. We prove these methods sharp, and compare them with existing methods.