A rigorous approach to evaluate the performance in optically pre-amplified differential phase-shift keying (DPSK) receivers with arbitrary optical and electrical filtering and using direct detection is presented. This approach is used to assess the degree of accuracy of the well known simplified approach that assumes a wide-band optical filter and an integrate-and-dump electrical filter. The performance results show that these two approaches can be used in a complementary way: the simplified approach is acceptable for time-bandwidth products larger or equal to 5, underestimating the receiver sensitivity by less than ~0.1 dB, while for time-bandwidth products smaller than 5 the rigorous approach should be used instead. It is shown that for a time-bandwidth product equal to 1 the simplified approach underestimate the receiver sensitivity by ~1.1 dB.