  Two families of q-Schur algebras associated to Hecke algebras of type D are
introduced, and related to a family used by Geck, Gruber and Hiss [10], [11].
We prove that the algebras in one family, called the q-Schur^{1.5} algebras,
are integrally free, stable under base change, and are standardly stratified if
the base field has odd characteristic. In the so-called linear prime case of
[10], [11], all three families give rise to Morita equivalent algebras. A final
section discusses a different example, and speculates on the direction of a
general theory.
