We have extended buffer gas cooling to trap atoms with small effective magnetic moments μeff. For μeff >= 3μB, 1012 atoms were buffer gas cooled, trapped, and thermally isolated in ultra high vacuum with roughly unit efficiency. For μeff < 3μB, the fraction of atoms remaining after full thermal isolation was limited by two processes: wind from the rapid removal of the buffer gas and desorbing helium films. In our current apparatus we trap atoms with μeff >= 1μB, and thermally isolate atoms with μeff >= 1.8μB. This triples the number of atomic species which can be buffer gas cooled and trapped in thermal isolation. Extrapolation of our results and simulations of the loss processes indicate that it is possible to trap and evaporatively cool 1μB atoms using buffer gas cooling.