It is currently under debate whether diamondlike BC2N may be harder than cubic BN (c-BN). Using the bond counting rule, we have performed an unconstrained search and identified a series of short period (111) superlattices that have much lower total energy than previously proposed structures. By examining the ideal strength of these pseudocubic boron-carbonitrides, we show that they are harder than c-BN. Our results are consistent with experimental findings, but in contrast with a recent theoretical study, which claimed that the BC2N is less hard than c-BN.