  Scharlemann and Schultens have shown that for any pair of knots K_1 and K_2,
w(K_1 # K_2) is greater than or equal to max{w(K_1),w(K_2)}. Scharlemann and
Thompson have given a scheme for possible examples where equality holds. Using
results of Scharlemann-Schultens, Rieck-Sedgwick and Thompson, it is shown that
for K the connected sum of mp-small knots and K' any non-trivial knot, w(K #
K')>w(K).
