  We study the problem of extending an abstract independence notion for types
of singletons (what Shelah calls a good frame) to longer types. Working in the
framework of tame abstract elementary classes, we show that good frames can
always be extended to types of independent sequences. As an application, we
show that tameness and a good frame imply Shelah's notion of dimension is
well-behaved, complementing previous work of Jarden and Sitton. We also improve
a result of the first author on extending a frame to larger models.
