We have considered the problem of protein design based on a model where the contact energy between amino acid residues is fitted phenomenologically using the Miyazawa-Jernigan matrix. Due to the simple form of the contact energy function, an analytical prescription is found which allows us to design energetically stable sequences for fixed amino acid residue compositions and target structures. The theoretically obtained sequences are compared with real proteins, and good correspondence is obtained. Finally, we discuss the effect of discrepancies in the procedure used to fit the contact energy on our theoretical predictions.