  In this work we study $S$-adic shifts generated by sequences of morphisms
that are constant-length. We call a sequence of constant-length morphisms
torsion-free if any prime divisor of one of the lengths is a divisor of
infinitely many of the lengths. We show that torsion-free directive sequences
generate shifts that enjoy the property of quasi-recognizability which can be
used as a substitute for recognizability. Indeed quasi-recognizable directive
sequences can be replaced by a recognizable directive sequence. With this, we
give a finer description of the spectrum of shifts generated by torsion-free
sequences defined on a sequence of alphabets of bounded size, in terms of
extensions of the notions of height and column number. We illustrate our
results throughout with examples that explain the subtleties that can arise.
