New eclipse timings of the Z Cam-type dwarf nova AY Psc were measured and the orbital ephemeris was revised. In addition, based on long-term AAVSO data, the outburst behaviors were also explored. Our analysis suggests that normal outbursts are quasi-periodic, with an amplitude of similar to 2.5 (+/- 0.1) mag and a period of similar to 18.3 (+/- 0.7) d. The amplitude vs. recurrence-time relation of AY Psc is discussed, and we conclude that this relationmay represent general properties of dwarf nova outbursts. The observed standstill ends with an outburst, which is inconsistent with the general picture of Z Camtype stars. This unusual behavior was considered to be related to mass- transfer outbursts. Moreover, the average luminosity is brighter during standstills than during outburst cycles. The changes in brightness mark variations in. M (over dot)(2) due to the fact that the disk of AY Psc is nearly steady state. M (over dot)(2) value was limited to the range from 6.35 x 10(-9) to 1.18 x 10(-8) M circle dot yr(-1). More detailed examination shows that there are a few small outbursts present during standstills. These events with amplitudes of similar to 0.5-0.9 mag are very similar to the stunted outbursts reported in some nova-like cataclysmic variables. We discussed several possible mechanisms and suggested that the most reasonable mechanism for these stunted outbursts is a changing mass- transfer rate.