The capacity region of general discrete-memoryless broadcast channels (DMBCs) with two receivers is an open problem of considerable research interest. The optimality of superposition coding in three specific cases of the DMBC is considered. For a DMBC with binary input, symmetric output and output cardinality at most 3, superposition coding is shown to be optimal. For equal-capacity DMBCs with any input cardinality, superposition coding is shown to be suboptimal if each channel has a capacity-achieving input distribution that is not capacity-achieving for the other channel. For an equal-capacity DMBC with binary input, superposition coding is shown to be optimal if and only if the two channels are more-capable comparable even without utput symmetry. These results improve upon the previously known conditions for optimality of superposition coding in DMBCs. © 2019 IEEE.