  We clarify what it means for two full dualities based on the same algebra to
be different. Our main theorem gives conditions on two different alter egos of
a finite algebra under which, if one yields a full duality, then the other does
too. We use this theorem to obtain a better understanding of several important
examples from the theory of natural dualities. Throughout the paper, a
fundamental role is played by the universal Horn theory of the dual classes.
