Some narcissistic power-sequence terraces for Z n are obtained, where n is the product of three distinct odd primes p, q and r such that lcm(p − 1, q − 1, r − 1) = (p − 1)(q − 1)(r − 1)/4 and p = 3. The paper's emphasis is on the strategy used to find such terraces, not on a formal presentation of the underlying mathematics. Special attention is paid to matryoshka terraces. Further, a combinatorial method is given for the construction of matryoshka Z n terraces for values n with any number of prime factors.