  In the study of asymptotic geometry in Banach spaces, a basic sequence which
gives rise to a spreading model has been called a good sequence. It is well
known that every normalized basic sequence in a Banach space has a subsequence
which is good. We investigate the assumption that every normalized block tree
relative to a basis has a branch which is good. This combinatorial property
turns out to be very strong and is equivalent to the space being $1$-asymptotic
$\ell_p$ for some $1\leq p\leq\infty$. We also investigate the even stronger
assumption that every block basic sequence of a basis is good. Finally, using
the Hindman-Milliken-Taylor theorem, we prove a stabilization theorem which
produces a basic sequence all of whose normalized constant coefficient block
basic sequences are good, and we present an application of this stabilization.
