  Let $K$ be a knot in a rational homology sphere $M$. This paper investigates
the question of when modifying $K$ by adding $m>0$ half-twists to two
oppositely-oriented strands, while keeping the rest of $K$ fixed, produces a
knot isotopic to $K$. Such a two-strand twist of order $m$, as we define it, is
a generalized crossing change when $m$ is even and a non-coherent band surgery
when $m=1$. A cosmetic two-strand twist on $K$ is a non-nugatory one that
produces an isotopic knot. We prove that fibered knots in $M$ admit no cosmetic
generalized crossing changes. Further, we show that if $K$ is fibered, then a
two-strand twist of odd order $m$ that is determined by a separating arc in a
fiber surface for $K$ can only be cosmetic if $m=\pm 1$.
  After proving these theorems, we further investigate cosmetic two-strand
twists of odd orders. Through two examples, we find that the second theorem
above becomes false if `separating' is removed, and that a key technical
proposition fails when the order equals 1. A closer look at an order-one
example, an instance of cosmetic band surgery on the unknot, reveals it to be
nearly trivial in a sense that we name `weakly nugatory'. We correct the
technical proposition to obtain a means of using double branched covers to show
that certain band surgeries are weakly nugatory. As an application, we prove
that every cosmetic band surgery on the unknot is of this type.

Geometric Topology