This paper considers two recently-proposed receivers, Tikh and DCT. Both receivers are computationally-efficient, iterative and designed to be robust against phase noise on the local oscillators of digital bandpass communication systems. The presented results build on our prior research. We discuss the initialization of the DCT receiver, explore reducing the computational complexity by simplifying the receiver scheduling and study the effect of a small frequency offset. Coded PSK signaling and additive white Gaussian noise are assumed.