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The modified Becke-Johnson exchange potential combined with local-density approximation correlation (mBJLDA) has recently attracted interest because it provides highly improved band gaps at a very low computational cost. In this work we performed an extensive investigation of the performance of the mBJLDA potential employing a norm-conserving pseudopotential plane-waves approach (mBJLDA@PP), as implemented in the abinit code, using a test set of 83 solids representing a wide range of semiconductors and insulators. Our results confirm the conclusion of our previous study that the number of electrons treated as valence in the pseudopotentials of the cations can have a significant impact on the calculated mBJLDA@PP band gaps. More specifically, while the use of typical pseudopotentials leads to accurate band gaps of certain systems, it yields significantly underestimated band gaps for other systems compared to experiment and to those of the all-electron mBJLDA (mBJLDA@AE) approach. The classes of the latter systems are identified, and this problem is resolved by including some outer core states as valence. The resulting mean absolute error in the calculated band gaps (compared to experiment) is of 0.46 eV, which is comparable to that of the mBJLDA@AE band gaps, reflecting the accuracy and reliability of the mBJLDA@PP approach for the band gap calculations.