  When high-energy single-hadron production takes place inside an identified
jet, there are important correlations between the fragmentation and phase-space
cuts. For example, when one-hadron yields are measured in on-resonance
B-factory data, a cut on the thrust event shape T is required to remove the
large b-quark contribution. This leads to a dijet final state restriction for
the light-quark fragmentation process. Here we complete our analysis of
unpolarized fragmentation of (light) quarks and gluons to a light hadron h with
energy fraction z in e+ e- -> dijet + h at the center-of-mass energy Q=10.58
GeV. In addition to the next-to-next-to-leading order resummation of logarithms
of 1-T, we include the next-to-leading order (NLO) nonsingular O(1-T)
contribution to the cross section, the resummation of threshold logarithms of
1-z, and the leading nonperturbative contribution to the soft function. Our
results for the correlations between fragmentation and the thrust cut are
presented in a way that can be directly tested against B-factory data. These
correlations are also observed in Pythia, but are surprisingly smaller at NLO.
