We prove that for all m, n, and $$\alpha $$ with $$1 \le \alpha \le f(m,n)$$, where f(m, n) is the state complexity of the concatenation operation, there exist a minimal m-state DFA A and a minimal n-state DFA B, both defined over an alphabet $$\varSigma $$ with $$|\varSigma |\le 2n+4$$, such that the minimal DFA for the language L(A)L(B) has exactly $$\alpha $$ states. This improves a similar result in the literature that uses an exponential alphabet.