  This paper deals exclusively with crossover designs for the purpose of
comparing t test treatments with a control treatment when the number of periods
is no larger than t+1. Among other results it specifies sufficient conditions
for a crossover design to be simultaneously A-optimal and MV-optimal in a very
large and appealing class of crossover designs. It is expected that these
optimal designs are highly efficient in the entire class of crossover designs.
Some computationally useful tools are given and used to build assorted small
optimal and efficient crossover designs. The model robustness of these newly
discovered crossover designs is discussed.
