  Calculations for inclusive J/psi production in Upsilon decay through the
color-octet mechanisms b\bar b[^3S_1, 1] -> c \bar c[^{2s+1}L_J, 8] + g are
presented. It is shown that these O(alpha^5_sv^4_c) contributions compete with
other color-octet mechanisms considered in the literature. A critical numerical
analysis of the color-octet contributions to Upsilon -> J/psi + X shows that
further work in this channel, both theoretical and experimental, is necessary
in order to clearly understand the significance of the color-octet component of
the c \bar c component inside the J/psi system.
