  Let Gamma be a group generated by two positive multi-twists. We give some
sufficient conditions for Gamma to be free or have no `unexpectedly reducible'
elements. For a group Gamma generated by two Dehn twists, we classify the
elements in Gamma which are multi-twists. As a consequence we are able to list
all the lantern-like relations in the mapping class groups. We classify groups
generated by powers of two Dehn twists which are free, or have no "unexpectedly
reducible" elements. In the end we pose similar problems for groups generated
by powers of n > 2 twists and give a partial result.
