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Apart from some (insoluble) subvarieties of JC5 , the jnC (just-non-Cross) varieties known so far comprise the following list: |L , A A , A T , A A A , where p, q and r are any three distinct primes. In a recent paper I gave a partial confirmation of the conjecture that the soluble jnC varieties all appear in this list. Here I show that a jnC variety is reducible if and only if it is soluble of finite exponent; this reduces the problem of classifying jnC varieties to finding the irreducibles ofdoi:10.1017/s0004972700046001 fatcat:b2mumlqfzzerlfx3hz3urn3y7u