Heegaard genus of the connected sum of m-small knots

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We prove that if K₁ ⊂ M₁,...,Kₙ ⊂ Mₙ are m-small knots in closed orientable 3-manifolds then the Heegaard genus of E(#ᵢ₌₁ⁿ Kᵢ) is strictly less than the sum of the Heegaard genera of the E(Kᵢ) (i=1,...,n) if and only if there exists a proper subset I of {1,...,n} so that #ᵢ ∈ ᵢ Kᵢ admits a primitive meridian. This generalizes the main result of Morimoto in morimoto1.