Abstract. We prove that if K 1 ⊂ M 1 , . . . , K n ⊂ M n are m-small knots in closed orientable 3-manifolds then the Heegaard genus of E(# n i=1 K i ) is strictly less than the sum of the Heegaard genera of the E(K i ) (i = 1, . . . , n) if and only if there exists a proper subset I of {1, . . . , n} so that # i∈I K i admits a primitive meridian. This generalizes the main result of Morimoto in [17].