  We present a variety of new results on finite sets A of integers for which
the sumset A+A is larger than the difference set A-A, so-called MSTD (more sums
than differences) sets. First we show that there is, up to affine
transformation, a unique MSTD subset of {\bf Z} of size 8. Secondly, starting
from some examples of size 9, we present several new constructions of infinite
families of MSTD sets. Thirdly we show that for every fixed ordered pair of
non-negative integers (j,k), as n -> \infty a positive proportion of the
subsets of {0,1,2,...,n} satisfy |A+A| = (2n+1) - j, |A-A| = (2n+1) - 2k.
